How to draw A ⊕ B ⊕ C as a Venn diagram?












17














You see my code and please answer my two questions:



documentclass{article}
usepackage{amsmath,amssymb,mathptmx}
usepackage{pstricks}
usepackage{pst-node}
usepackage{auto-pst-pdf}
begin{document}
begin{pspicture}[showgrid](-3,-3)(8,8)%[linestyle=none]
psclip{%
pscircle(0,0){3}
pscircle(4,0){3} }
pscircle[fillcolor=blue,fillstyle=solid](2,3){3}
endpsclip
pscircle(0,0){3}
pscircle(4,0){3}
pscircle(2,3){3}
end{pspicture}
end{document}


The output picture:



enter image description here



Picture 1:



enter image description here



Its code (use TikZ):



documentclass{article}
usepackage{tikz}

begin{document}
begin{tikzpicture}
fill[blue,even odd rule] (0,0) circle (3) (4,0) circle (3) (2,3) circle (3);
end{tikzpicture}


My questions:




  • How to make my picture like Picture 1? Truly I don't know how to fill color to it.


  • (After completing the previous question) Do you see the TikZ code of Picture 1? Look at the important option even odd rule. Do PStricks have the equivalent command, macro,.. as TikZ?




Notice: I prefer PStricks to TikZ but sometimes I recognize the TikZ code is better.




Sorry if I make you being uncomfortable.



UPDATE:



New package "pst-venn" in http://tug.org/PSTricks/main.cgi










share|improve this question
























  • @ Dũng Vũ Thank you.
    – chishimotoji
    Nov 30 at 6:39










  • Wonderful package!
    – JouleV
    Dec 6 at 10:15










  • Exactly........................!
    – chishimotoji
    Dec 6 at 10:20
















17














You see my code and please answer my two questions:



documentclass{article}
usepackage{amsmath,amssymb,mathptmx}
usepackage{pstricks}
usepackage{pst-node}
usepackage{auto-pst-pdf}
begin{document}
begin{pspicture}[showgrid](-3,-3)(8,8)%[linestyle=none]
psclip{%
pscircle(0,0){3}
pscircle(4,0){3} }
pscircle[fillcolor=blue,fillstyle=solid](2,3){3}
endpsclip
pscircle(0,0){3}
pscircle(4,0){3}
pscircle(2,3){3}
end{pspicture}
end{document}


The output picture:



enter image description here



Picture 1:



enter image description here



Its code (use TikZ):



documentclass{article}
usepackage{tikz}

begin{document}
begin{tikzpicture}
fill[blue,even odd rule] (0,0) circle (3) (4,0) circle (3) (2,3) circle (3);
end{tikzpicture}


My questions:




  • How to make my picture like Picture 1? Truly I don't know how to fill color to it.


  • (After completing the previous question) Do you see the TikZ code of Picture 1? Look at the important option even odd rule. Do PStricks have the equivalent command, macro,.. as TikZ?




Notice: I prefer PStricks to TikZ but sometimes I recognize the TikZ code is better.




Sorry if I make you being uncomfortable.



UPDATE:



New package "pst-venn" in http://tug.org/PSTricks/main.cgi










share|improve this question
























  • @ Dũng Vũ Thank you.
    – chishimotoji
    Nov 30 at 6:39










  • Wonderful package!
    – JouleV
    Dec 6 at 10:15










  • Exactly........................!
    – chishimotoji
    Dec 6 at 10:20














17












17








17


3





You see my code and please answer my two questions:



documentclass{article}
usepackage{amsmath,amssymb,mathptmx}
usepackage{pstricks}
usepackage{pst-node}
usepackage{auto-pst-pdf}
begin{document}
begin{pspicture}[showgrid](-3,-3)(8,8)%[linestyle=none]
psclip{%
pscircle(0,0){3}
pscircle(4,0){3} }
pscircle[fillcolor=blue,fillstyle=solid](2,3){3}
endpsclip
pscircle(0,0){3}
pscircle(4,0){3}
pscircle(2,3){3}
end{pspicture}
end{document}


The output picture:



enter image description here



Picture 1:



enter image description here



Its code (use TikZ):



documentclass{article}
usepackage{tikz}

begin{document}
begin{tikzpicture}
fill[blue,even odd rule] (0,0) circle (3) (4,0) circle (3) (2,3) circle (3);
end{tikzpicture}


My questions:




  • How to make my picture like Picture 1? Truly I don't know how to fill color to it.


  • (After completing the previous question) Do you see the TikZ code of Picture 1? Look at the important option even odd rule. Do PStricks have the equivalent command, macro,.. as TikZ?




Notice: I prefer PStricks to TikZ but sometimes I recognize the TikZ code is better.




Sorry if I make you being uncomfortable.



UPDATE:



New package "pst-venn" in http://tug.org/PSTricks/main.cgi










share|improve this question















You see my code and please answer my two questions:



documentclass{article}
usepackage{amsmath,amssymb,mathptmx}
usepackage{pstricks}
usepackage{pst-node}
usepackage{auto-pst-pdf}
begin{document}
begin{pspicture}[showgrid](-3,-3)(8,8)%[linestyle=none]
psclip{%
pscircle(0,0){3}
pscircle(4,0){3} }
pscircle[fillcolor=blue,fillstyle=solid](2,3){3}
endpsclip
pscircle(0,0){3}
pscircle(4,0){3}
pscircle(2,3){3}
end{pspicture}
end{document}


The output picture:



enter image description here



Picture 1:



enter image description here



Its code (use TikZ):



documentclass{article}
usepackage{tikz}

begin{document}
begin{tikzpicture}
fill[blue,even odd rule] (0,0) circle (3) (4,0) circle (3) (2,3) circle (3);
end{tikzpicture}


My questions:




  • How to make my picture like Picture 1? Truly I don't know how to fill color to it.


  • (After completing the previous question) Do you see the TikZ code of Picture 1? Look at the important option even odd rule. Do PStricks have the equivalent command, macro,.. as TikZ?




Notice: I prefer PStricks to TikZ but sometimes I recognize the TikZ code is better.




Sorry if I make you being uncomfortable.



UPDATE:



New package "pst-venn" in http://tug.org/PSTricks/main.cgi







color pstricks






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited Dec 6 at 10:02

























asked Nov 30 at 6:08









chishimotoji

810316




810316












  • @ Dũng Vũ Thank you.
    – chishimotoji
    Nov 30 at 6:39










  • Wonderful package!
    – JouleV
    Dec 6 at 10:15










  • Exactly........................!
    – chishimotoji
    Dec 6 at 10:20


















  • @ Dũng Vũ Thank you.
    – chishimotoji
    Nov 30 at 6:39










  • Wonderful package!
    – JouleV
    Dec 6 at 10:15










  • Exactly........................!
    – chishimotoji
    Dec 6 at 10:20
















@ Dũng Vũ Thank you.
– chishimotoji
Nov 30 at 6:39




@ Dũng Vũ Thank you.
– chishimotoji
Nov 30 at 6:39












Wonderful package!
– JouleV
Dec 6 at 10:15




Wonderful package!
– JouleV
Dec 6 at 10:15












Exactly........................!
– chishimotoji
Dec 6 at 10:20




Exactly........................!
– chishimotoji
Dec 6 at 10:20










5 Answers
5






active

oldest

votes


















19














A PSTricks solution just for fun!



Answer 1



documentclass[pstricks]{standalone}
begin{document}
begin{pspicture}(-5,-5)(5,5)
pscustom[fillstyle=eofill,fillcolor=blue]
{
pscircle(1.5;90){3}
pscircle(1.5;-30){3}
pscircle(1.5;210){3}
}
end{pspicture}
end{document}


enter image description here



The stroke color is left black just for a trivial reason.



Cartesian coordinates are used in response to the request.



documentclass[pstricks]{standalone}
begin{document}
begin{pspicture}(-5,-5)(5,5)
pscustom[fillstyle=eofill,fillcolor=blue]
{
pscircle(0,1.5){3}
pscircle(1.29,-0.75){3}
pscircle(-1.29,-0.75){3}
}
end{pspicture}
end{document}


Answer 2



Non-zero winding rule:



documentclass[pstricks,border=12pt]{standalone}
begin{document}
begin{pspicture}[showgrid=t](-3,-3)(3,3)
pscustom[fillstyle=solid,fillcolor=red]
{
pscircle{1}
pscircle{2}
}
end{pspicture}
end{document}


enter image description here



Non-zero winding rule:



documentclass[pstricks,border=12pt]{standalone}
begin{document}
begin{pspicture}[showgrid=t](-3,-3)(3,3)
pscustom[fillstyle=solid,fillcolor=red]
{
psarcn(0,0){1}{360}{0}
pscircle{2}
}
end{pspicture}
end{document}


enter image description here



Even-odd rule:



documentclass[pstricks,border=12pt]{standalone}
begin{document}
begin{pspicture}[showgrid=t](-3,-3)(3,3)
pscustom[fillstyle=eofill,fillcolor=red]
{
pscircle{1}
pscircle{2}
}
end{pspicture}
end{document}


enter image description here






share|improve this answer































    16





    +500









    Here is an answer based on the one by @Thomas. Differences




    • the "elementary" regions I, II, ..., VIII are not numbered the same. My numbering is that "N" is the Roman number of "n+1" where "n" in binary is "abc", and the region is intersection of A or not A with B or not B with C or not C according to a, b, c = 0 or 1. (Boolean logic)


    • the macro needs only one input: a TeX formula for the set. Please enrich the syntax by adding suitable definitions converting TeX math macros into Boolean logic notation, as understood by xintexpr


    • I have dropped all fancy customization of colors, but xparse virtuosos will add the fancy optional arguments to re-install it if needed.



    Thus, the big point here is that xintexpr computes automatically from the TeX typesetting formula which regions are to be filled in diagram.




    attention to setminus it must be used either with parentheses setminus (...) or without but then with only one letter setminus A
    ok, setminus Acap B not ok, because the translation here to xintexpr
    boolean will do naively something equivalent to and not(A) and B, not the expected and not(A and B). In short, you must treat setminus as having maximally tying precedence.




    documentclass[pstricks, border=10pt]{standalone}
    usepackage{pst-node}
    usepackage{xparse,xintexpr}

    defKOEA{1.9,2.2}
    defFOEA{1.4,1}

    defKOEB{3.3,2.2}
    defFOEB{1.2,1}

    defKOEC{2.75,1.4}
    defFOEC{1.4,1}

    defKOEO{2.5,2}
    defFOEO{2.5,2.0}

    NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
    IfBooleanTF{#1}{%
    psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
    psellipse(KOEA)(FOEA)}%
    }

    NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
    IfBooleanTF{#1}{%
    psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
    psellipse(KOEB)(FOEB)}%
    }

    NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
    IfBooleanTF{#1}{%
    psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
    psellipse(KOEC)(FOEC)}%
    }

    NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
    IfBooleanTF{#1}{%
    psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
    psellipse(KOEO)(FOEO)}%
    }

    NewDocumentCommand{EndeEllipsen}{sm}{%
    EreignisOmega%
    pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
    pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
    EreignisA
    EreignisB
    EreignisC
    rput[t](E){#2}%
    IfBooleanF{#1}{%
    rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
    rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
    rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
    rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
    }%
    }

    NewDocumentCommand{codeclip}{m}{%
    pscustom[linestyle=none]{%
    code{/clip /eoclip load def}%
    psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
    #1
    }%
    }

    %ExplSyntaxOn
    % We could use some automated macro creation but well
    % 000
    NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    }%
    codeclip{%
    EreignisB
    }%
    codeclip{%
    EreignisC
    }%
    }%
    EreignisOmega*[#1][#2]%
    endpsclip
    }%
    % 001
    NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    }%
    codeclip{%
    EreignisB
    }%
    }%
    EreignisC*[#1][#2]%
    endpsclip
    }
    % 010
    NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    }%
    codeclip{%
    EreignisC
    }%
    }%
    EreignisB*[#1][#2]%
    endpsclip
    }
    % 011
    NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisB
    EreignisC
    }%
    codeclip{%
    EreignisA
    }%
    }%
    EreignisB*[#1][#2]%
    EreignisC*[#1][#2]%
    endpsclip
    }
    % 100
    NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisB
    }%
    codeclip{%
    EreignisC
    }%
    }%
    EreignisA*[#1][#2]%
    endpsclip
    }
    % 101
    NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    EreignisC
    }%
    codeclip{%
    EreignisB
    }%
    }%
    EreignisA*[#1][#2]%
    EreignisC*[#1][#2]%
    endpsclip
    }
    % 110
    NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    EreignisB
    }%
    codeclip{%
    EreignisC
    }%
    }%
    EreignisA*[#1][#2]%
    EreignisB*[#1][#2]%
    endpsclip
    }
    % 111
    NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    EreignisB
    }%
    codeclip{%
    EreignisA
    EreignisC
    }%
    codeclip{%
    EreignisB
    EreignisC
    }%
    }%
    EreignisA*[#1][#2]%
    EreignisB*[#1][#2]%
    EreignisC*[#1][#2]%
    endpsclip
    }
    %ExplSyntaxOff

    %xintverbosetrue
    makeatletter
    newcommandVennFromTeX[1]{%
    VennFromTeX@main #1%
    }%
    defVennFromTeX@main$#1${%
    begingroup
    xintglobaldefstrue
    defoverline##1{!(##1)}% or not(##1)
    defcap{&&}% or 'and'
    defcup{||}% or 'or'
    defoplus{ 'xor' }%
    defsetminus##1{ifx(##1&&!(else &&!(##1)fi}%
    letbiglempty
    letbigrempty
    % ....
    % (add above all needed extra definitions: letBiglempty etc...)
    xintdeffunc MyBool(A, B, C) := #1;% #1 must use A, B, C only
    endgroup
    % we could make a loop here (using @Roman), but let's stay simple
    % I trust xparse experts can wrap this up in macros allowing to customize
    % the colors
    % ATTENTION THAT THESE arealI...VIII ARE NOT THE SAME AS IN @THOMAS ANSWER
    xintifboolexpr{MyBool(0, 0, 0)}{arealI[cyan][0.8]}{}%
    xintifboolexpr{MyBool(0, 0, 1)}{arealII[cyan][0.8]}{}%
    xintifboolexpr{MyBool(0, 1, 0)}{arealIII[cyan][0.8]}{}%
    xintifboolexpr{MyBool(0, 1, 1)}{arealIV[cyan][0.8]}{}%
    xintifboolexpr{MyBool(1, 0, 0)}{arealV[cyan][0.8]}{}%
    xintifboolexpr{MyBool(1, 0, 1)}{arealVI[cyan][0.8]}{}%
    xintifboolexpr{MyBool(1, 1, 0)}{arealVII[cyan][0.8]}{}%
    xintifboolexpr{MyBool(1, 1, 1)}{arealVIII[cyan][0.8]}{}%
    EndeEllipsen{$#1$}%
    }%
    makeatother

    begin{document}

    %testing if I, II, ..., VIII are as expected
    % makeatletter
    % xintFor*#1in{xintSeq{0}{7}}do{%
    % begin{pspicture}(0,-1)(5,4)
    % rput(2,0){thenumexpr1+#1}
    % @nameuse{areal@Roman{numexpr1+#1}}[cyan][0.8]
    % EndeEllipsen{}
    % end{pspicture}
    % }%
    % end{document}


    begin{pspicture}(0,-1)(5,4)
    VennFromTeX{$Acap Bcap C$}%
    end{pspicture}

    begin{pspicture}(0,-1)(5,4)
    VennFromTeX{$Acap (Bcup C)$}
    end{pspicture}

    begin{pspicture}(0,-1)(5,4)
    VennFromTeX{$(overline{A}cap overline{B})cup C$}
    end{pspicture}

    begin{pspicture}(0,-1)(5,4)
    VennFromTeX{$overline{A}setminus (Bcap C)$}
    end{pspicture}

    begin{pspicture}(0,-1)(5,4)
    VennFromTeX{$(overline{A}setminus B)cap C$}
    end{pspicture}

    begin{pspicture}(0,-1)(5,4)
    VennFromTeX{$(Asetminus B)cup (Bcap C)$}
    end{pspicture}

    begin{pspicture}(0,-1)(5,4)
    VennFromTeX{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
    end{pspicture}

    begin{pspicture}(0,-1)(5,4)
    VennFromTeX{$Aoplus Boplus C$}
    end{pspicture}

    end{document}


    Produces



    enter image description here



    enter image description here



    enter image description here



    enter image description here



    enter image description here



    enter image description here



    enter image description here



    enter image description here







    Here is code to generate all 256 Venn diagrams. Just insert it in body of above document and don't forget to add usepackage{xintbinhex} to preamble.



    % generating all graphics

    % 0<= n <= 255 has eight binary digits
    % abcdefgh
    % a=1 -> region VIII is included (A cap B cap C)
    % b=1 -> region VII is included
    % ...
    % h=1 -> region I is included (overline{A}cap overline{B} cap overline{C})
    % We want also to describe the region as a formula...
    % We could use 8 xintFor loops #1, ..., #8, but then
    % we still need to convert #1*7 to binary, #2*6, #3*5 etc...
    % I thus use xintbinhex per convenience but ifodd would be enough
    % As I use xintbinhex, I also use a single xintFor* loop

    %defgobbleone#1{}%
    defgobbletwo#1#2{}%
    xintFor* #1 in {xintSeq{0}{255}}:
    {%
    xintDigitsOfxintDecToBin{thenumexpr256+#1relax}toRegions
    % due to leading 1 there will be a shift of indexing in Regions
    edefx{xintifboolexpr{Regions{thenumexpr9-0}}% 000
    {unexpanded{allowbreakcup
    overline{A}capoverline{B}capoverline{C}}}%
    {}%
    xintifboolexpr{Regions{9-1}}% 001
    {unexpanded{allowbreakcup overline{A}capoverline{B}cap C}}%
    {}%
    xintifboolexpr{Regions{9-2}}% 010
    {unexpanded{allowbreakcup overline{A}cap B capoverline{C}}}%
    {}%
    xintifboolexpr{Regions{9-3}}% 011
    {unexpanded{allowbreakcup overline{A} cap B cap C}}%
    {}%
    xintifboolexpr{Regions{9-4}}% 100
    {unexpanded{allowbreakcup Acap overline{B}cap overline{C}}}%
    {}%
    xintifboolexpr{Regions{9-5}}% 101
    {unexpanded{allowbreakcup Acap overline{B}cap C}}%
    {}%
    xintifboolexpr{Regions{9-6}}% 110
    {unexpanded{allowbreakcup Acap Bcap overline{C}}}%
    {}%
    xintifboolexpr{Regions{9-7}}% 111
    {unexpanded{allowbreakcup Acap B cap C}}%
    {}%
    }%
    xintifForFirst{defx{emptyset}}
    {oodefx{expandaftergobbletwox}}%
    begin{pspicture}(0,-2)(5,4)
    % I will leave here each Region as individual call, so a color can
    % be added by modifying this code
    xintifboolexpr{Regions{9-0}}{arealI[cyan][0.8]}{}%
    xintifboolexpr{Regions{9-1}}{arealII[cyan][0.8]}{}%
    xintifboolexpr{Regions{9-2}}{arealIII[cyan][0.8]}{}%
    xintifboolexpr{Regions{9-3}}{arealIV[cyan][0.8]}{}%
    xintifboolexpr{Regions{9-4}}{arealV[cyan][0.8]}{}%
    xintifboolexpr{Regions{9-5}}{arealVI[cyan][0.8]}{}%
    xintifboolexpr{Regions{9-6}}{arealVII[cyan][0.8]}{}%
    xintifboolexpr{Regions{9-7}}{arealVIII[cyan][0.8]}{}%
    EndeEllipsen{parbox{4cm}{centering$x$}}%
    end{pspicture}%
    }%


    Defect: the description of the set is as a disjoint union of atomic events. There might be some canonical shorter description but I never really thought about it. For example one of those diagram will represent $Omegasetminus A$ but this not the way it will be legended.



    Here is how this example comes out (on page 16 of document with nothing else, i.e. it corresponds to #1 = 15 in the loop, 15=1111 means to keep atomic events 0=000, 1=001, 2=010, 3=011, which is complement of A in Omega.



    enter image description here







    Here is now with 4 sets.



    This time, with TikZ code (I know neither PSTricks nor TikZ and can only survive from copying pre-existing drawing instructions; in this case I started from https://tex.stackexchange.com/a/100091/4686 by @JohnHammersley in 2013).



    First I include an image of all atomic events, which are the regions to which the Atomic... macros in code next refer. (this was done for checking while preparing answer)



    enter image description here



    Here is the code for VennFromTeX, use it as VennFromTeX{$ set formula with A, B, C, D $}. Same instructions as above for three sets.
    (one may wish to enlarge the syntax for example by allowing use of U or Omega and defining it in xintexpr to be simply 1, and similarly emptyset could be defined to be 0).



    documentclass[12pt, tikz, border=10pt]{standalone}

    usepackage{tikz}

    usetikzlibrary{positioning,shapes.geometric}

    usepackage{xintexpr}% for VennFromTeX


    % For drawing
    deffirstellip{(-1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
    defsecondellip{(-0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
    defthirdellip{(0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}
    deffourthellip{(1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}

    defbounding{(-5,-3) rectangle (5,4)}

    % Elementary sets
    % ABCD
    % abcd a, b, c, d in {0, 1}
    defAtomic{% 0000
    begin{scope}[even odd rule]% exterior
    clip firstellip (-5,-5) rectangle (5,5);
    clip secondellip (-5,-5) rectangle (5,5);
    clip thirdellip (-5,-5) rectangle (5,5);
    clip fourthellip (-5,-5) rectangle (5,5);
    fill[yellow] bounding;
    end{scope}
    }%
    defAtomici{% 0001
    begin{scope}[even odd rule]% fourth ellipse corner
    clip firstellip (-5,-5) rectangle (5,5);
    clip secondellip (-5,-5) rectangle (5,5);
    clip thirdellip (-5,-5) rectangle (5,5);
    fill[yellow] fourthellip;
    end{scope}
    }%
    defAtomicii{% 0010
    begin{scope}[even odd rule]% third ellipse corner
    clip firstellip (-5,-5) rectangle (5,5);
    clip secondellip (-5,-5) rectangle (5,5);
    clip fourthellip (-5,-5) rectangle (5,5);
    fill[yellow] thirdellip;
    end{scope}
    }%
    defAtomiciii{% 0011
    begin{scope}[even odd rule]%
    clip firstellip (-5,-5) rectangle (5,5);
    clip secondellip (-5,-5) rectangle (5,5);
    clip fourthellip;
    fill[yellow] thirdellip;
    end{scope}
    }%
    defAtomiciv{% 0100
    begin{scope}[even odd rule]% second ellipse corner
    clip firstellip (-5,-5) rectangle (5,5);
    clip thirdellip (-5,-5) rectangle (5,5);
    clip fourthellip (-5,-5) rectangle (5,5);
    fill[yellow] secondellip;
    end{scope}
    }%
    defAtomicv{% 0101
    begin{scope}[even odd rule]%
    clip firstellip (-5,-5) rectangle (5,5);
    clip thirdellip (-5,-5) rectangle (5,5);
    clip fourthellip;
    fill[yellow] secondellip;
    end{scope}
    }%
    defAtomicvi{% 0110
    begin{scope}[even odd rule]%
    clip firstellip (-5,-5) rectangle (5,5);
    clip thirdellip;
    clip fourthellip (-5,-5) rectangle (5,5);
    fill[yellow] secondellip;
    end{scope}
    }%
    defAtomicvii{% 0111
    begin{scope}[even odd rule]%
    clip firstellip (-5,-5) rectangle (5,5);
    clip thirdellip;
    clip fourthellip;
    fill[yellow] secondellip;
    end{scope}
    }%
    defAtomicviii{% 1000
    begin{scope}[even odd rule]%
    clip secondellip (-5,-5) rectangle (5,5);
    clip thirdellip (-5,-5) rectangle (5,5);
    clip fourthellip (-5,-5) rectangle (5,5);
    fill[yellow] firstellip;
    end{scope}
    }%
    defAtomicix{% 1001
    begin{scope}[even odd rule]%
    clip secondellip (-5,-5) rectangle (5,5);
    clip thirdellip (-5,-5) rectangle (5,5);
    clip fourthellip;
    fill[yellow] firstellip;
    end{scope}
    }%
    defAtomicx{% 1010
    begin{scope}[even odd rule]%
    clip secondellip (-5,-5) rectangle (5,5);
    clip thirdellip;
    clip fourthellip (-5,-5) rectangle (5,5);
    fill[yellow] firstellip;
    end{scope}
    }%
    defAtomicxi{% 1011
    begin{scope}[even odd rule]%
    clip secondellip (-5,-5) rectangle (5,5);
    clip thirdellip;
    clip fourthellip;
    fill[yellow] firstellip;
    end{scope}
    }%
    defAtomicxii{% 1100
    begin{scope}[even odd rule]%
    clip secondellip;
    clip thirdellip (-5,-5) rectangle (5,5);
    clip fourthellip (-5,-5) rectangle (5,5);
    fill[yellow] firstellip;
    end{scope}
    }%
    defAtomicxiii{% 1101
    begin{scope}[even odd rule]%
    clip secondellip;
    clip thirdellip (-5,-5) rectangle (5,5);
    clip fourthellip;
    fill[yellow] firstellip;
    end{scope}
    }%
    defAtomicxiv{% 1110
    begin{scope}[even odd rule]%
    clip secondellip;
    clip thirdellip;
    clip fourthellip (-5,-5) rectangle (5,5);
    fill[yellow] firstellip;
    end{scope}
    }%
    defAtomicxv{% 1111
    begin{scope}[even odd rule]%
    clip secondellip;
    clip thirdellip;
    clip fourthellip;
    fill[yellow] firstellip;
    end{scope}
    }%

    makeatletter
    newcommandVennFromTeX[1]{VennFromTeX@main #1}%

    defVennFromTeX@main$#1${%
    begingroup
    xintglobaldefstrue
    defoverline##1{!(##1)}% or not(##1)
    defcap{&&}% or 'and'
    defcup{||}% or 'or'
    defoplus{ 'xor' }%
    defsetminus##1{ifx(##1&&!(else &&!(##1)fi}%
    letbiglempty
    letbigrempty
    % ....
    % (add above all needed extra definitions: letBiglempty etc...)
    xintdeffunc MyBool(A, B, C, D) := #1;% #1 must use A, B, C, Donly
    endgroup
    begin{tikzpicture}

    xintFor* ##1 in {01}:
    {%
    xintFor* ##2 in {01}:
    {%
    xintFor* ##3 in {01}:
    {%
    xintFor* ##4 in {01}:
    {%
    xintifboolexpr{MyBool(##1, ##2, ##3, ##4)}
    {csname
    Atomicromannumeralnumexpr##1*8+##2*4+##3*2+##4endcsname}%
    {}%
    }%
    }%
    }%
    }%
    draw bounding;

    % fill[white] firstellip;
    % fill[white] secondellip;
    % fill[white] thirdellip;
    % fill[white] fourthellip;

    draw firstellip node [label={[xshift=-2cm, yshift=-0.9cm]$A$}] {};
    draw secondellip node [label={[xshift=-2.1cm, yshift=2.1cm]$B$}] {};
    draw thirdellip node [label={[xshift=2.1cm, yshift=2.1cm]$C$}] {};
    draw fourthellip node [label={[xshift=2cm, yshift=-0.9cm]$D$}] {};

    draw bounding node [label=below left:$U$] {};

    draw (0, 0) node [yshift=+4.4cm] {$#1$};

    end{tikzpicture}
    }%
    makeatother
    begin{document}

    % xintverbosetrue

    VennFromTeX{$Acap Bcap Ccap D$}

    VennFromTeX{$(Acap B)cup (Ccap D)$}

    VennFromTeX{$(overline{A}cupoverline{B})cap(overline{C}cupoverline{D})$}

    % attention to use parentheses for disambiguating setminus

    VennFromTeX{$(Acup B cup C) setminus(Bcup Ccup D)$}

    VennFromTeX{$(Acup B cup C) cap (Bcup Ccup D)$}

    VennFromTeX{$((Asetminus (Bcup Ccup D)) cup Bcap Ccap
    D)setminus (Acap Bcap Ccap D)$}

    end{document}


    Be careful to read the caveat top regarding usage of setminus in input.



    enter image description here



    enter image description here



    enter image description here



    enter image description here



    enter image description here



    enter image description here



    and finally



    enter image description here






    share|improve this answer























    • (+1) Thank you for your answer!
      – chishimotoji
      Dec 2 at 11:27










    • (+1) Wow, fantastic!
      – Thomas
      Dec 2 at 11:34






    • 1




      Encyclopedic answer
      – Diaa
      Dec 2 at 11:38










    • careful in first part of answer when inputting a long formula that it some parts may be cut off the page, check the parbox in second part how to work around that, and I also increased the vertical dimension.
      – jfbu
      Dec 2 at 12:46






    • 2




      @ArtificialStupidity I have to get dinner but just give me time to learn PSTricks and I can do with 4 sets afterwards...
      – jfbu
      Dec 2 at 18:39



















    12














    documentclass[pstricks]{standalone}
    begin{document}
    begin{pspicture}(-5,-5)(5,5)
    pscustom[fillstyle=eofill,fillcolor=blue,linecolor=blue]{%
    pscircle(1.5;90){3}
    pscircle(1.5;-30){3}
    pscircle(1.5;210){3}
    }
    end{pspicture}
    end{document}


    enter image description here



    Some other simple example:



    documentclass[pstricks]{standalone}
    usepackage{pstricks}
    begin{document}
    begin{pspicture}(-3.2,-3.2)(3.2,3.2)
    pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
    psclip{pscircle(-1,0.5){1.5}% these object(s) will clip
    pscircle(1,0.5){1.5}}
    pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}% from this object
    endpsclip
    pscircle(-1,0.5){1.5}% to get the clipped circle lines
    pscircle(0,-1){1.5}
    pscircle(1,0.5){1.5}
    end{pspicture}

    begin{pspicture}(-3.2,-3.2)(3.2,3.2)
    pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
    psclip{pscircle(-1,0.5){1.5}}
    pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}
    pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
    endpsclip
    pscircle(-1,0.5){1.5}
    pscircle(0,-1){1.5}
    pscircle(1,0.5){1.5}
    end{pspicture}

    begin{pspicture}(-3.2,-3.2)(3.2,3.2)
    pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
    psclip{pscircle(0,-1){1.5}}
    pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
    pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
    endpsclip
    pscircle(-1,0.5){1.5}
    pscircle(0,-1){1.5}
    pscircle(1,0.5){1.5}
    end{pspicture}

    begin{pspicture}(-3.2,-3.2)(3.2,3.2)
    pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
    psclip{pscircle(0,-1){1.5}}
    pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
    endpsclip
    pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
    pscircle(0,-1){1.5}
    pscircle(1,0.5){1.5}
    end{pspicture}

    end{document}


    enter image description hereenter image description here






    share|improve this answer



















    • 1




      I haven't known that there is a option as " fillstyle=eofill " before. It doesn't within PStrick User's Guide.
      – chishimotoji
      Nov 30 at 8:38






    • 1




      tug.org/PSTricks/main.cgi?file=Examples/Box/boxfill#2
      – Herbert
      Nov 30 at 11:20










    • I am really impressived by your code. Only with psclip,pscustom, you created some the interesting result. I have deleted more three comments before. May be my knowledge about psclip is not enough to generate several thing which I want. :((((
      – chishimotoji
      Dec 2 at 15:38








    • 2




      clipping is nothing else than taking a knife let it go along a circle or two corcles and cut everything from a given cake. psclip{the way of the knife} ... the cake .. endpsclip
      – Herbert
      Dec 2 at 15:41



















    9














    A TikZ solution for comparison purposes.



    documentclass{article}
    usepackage{tikz}
    begin{document}
    begin{tikzpicture}
    draw[even odd rule,fill=blue](0,0)circle(3)(4,0)circle(3)(2,3)circle(3);
    end{tikzpicture}
    end{document}


    Venn



    Update: To answer @ArtificialStupidity's comment



    Here is a solution with different coordinate points from those of the question asked by the OP. The centres of the circles form an equilateral triangle here.



    documentclass{article}
    usepackage{tikz}
    begin{document}
    begin{tikzpicture}
    draw[even odd rule,fill=blue](0,0)circle(3)(3,0)circle(3)(60:3)circle(3);
    end{tikzpicture}
    end{document}


    venn-2






    share|improve this answer























    • @ArtificialStupidity Yes, as in the figure given as an example by the OP. I didn't change the coordinates.
      – AndréC
      Nov 30 at 12:05










    • +1 for the equilateral triangle Δ
      – stendarr
      Nov 30 at 14:03



















    8














    With this definitions every surface can be colored.



    documentclass[pstricks]{standalone}
    usepackage{pst-node}
    usepackage{xparse,xintexpr}

    defradiusK{xinttheiexpr[6] 2*sqrt(3)/3relax}

    defKOEA{2.5,2}
    defFOEA{radiusK,radiusK}

    defKOEB{2,1}
    defFOEB{radiusK,radiusK}

    defKOEC{3,1}
    defFOEC{radiusK,radiusK}

    defKOEO{2.5,1.375}
    defFOEO{2.5,2.5}

    %uncomment the following lines to have ellipses
    %defKOEA{1.9,2.2}
    %defFOEA{1.4,1}
    %
    %defKOEB{3.3,2.2}
    %defFOEB{1.2,1}
    %
    %defKOEC{2.75,1.4}
    %defFOEC{1.4,1}
    %
    %defKOEO{2.5,2}
    %defFOEO{2.5,2.0}

    NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
    IfBooleanTF{#1}{%
    psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
    psellipse(KOEA)(FOEA)}%
    }

    NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
    IfBooleanTF{#1}{%
    psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
    psellipse(KOEB)(FOEB)}%
    }

    NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
    IfBooleanTF{#1}{%
    psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
    psellipse(KOEC)(FOEC)}%
    }

    NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
    IfBooleanTF{#1}{%
    psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
    psellipse(KOEO)(FOEO)}%
    }

    NewDocumentCommand{EndeEllipsen}{sm}{%
    EreignisOmega%
    pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
    pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
    EreignisA
    EreignisB
    EreignisC
    rput[t](E){#2}%
    IfBooleanF{#1}{%
    rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
    rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
    rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
    rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
    }%
    }

    NewDocumentCommand{codeclip}{m}{%
    pscustom[linestyle=none]{%
    code{/clip /eoclip load def}%
    psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
    #1
    }%
    }

    NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    }%
    codeclip{%
    EreignisB
    }%
    codeclip{%
    EreignisC
    }%
    }%
    EreignisOmega*[#1][#2]%
    endpsclip
    }

    NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisB
    EreignisC
    }%
    codeclip{%
    EreignisC
    }%
    }%
    EreignisA*[#1][#2]%
    endpsclip
    }

    NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    EreignisB
    EreignisC
    }%
    codeclip{%
    EreignisC
    }%
    }%
    EreignisA*[#1][#2]%
    endpsclip
    }

    NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    EreignisC
    }%
    codeclip{%
    EreignisC
    }%
    }%
    EreignisB*[#1][#2]%
    endpsclip
    }

    NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    EreignisB
    EreignisC
    }%
    codeclip{%
    EreignisB
    }%
    }%
    EreignisA*[#1][#2]%
    endpsclip
    }

    NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
    psclip{EreignisB}
    psclip{EreignisC}%
    EreignisA*[#1][#2]%
    endpsclip
    endpsclip
    }

    NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    EreignisB
    EreignisC
    }%
    codeclip{%
    EreignisA
    }%
    }%
    EreignisC*[#1][#2]%
    endpsclip
    }

    NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    EreignisB
    }%
    codeclip{%
    EreignisB
    }%
    }%
    EreignisC*[#1][#2]%
    endpsclip
    }

    begin{document}


    begin{pspicture}[shift=-4](0,-1)(5,4)
    arealI
    EndeEllipsen*{$Asetminus C$}
    end{pspicture}

    begin{pspicture}[shift=-4](0,-1)(5,4)
    arealVI
    EndeEllipsen*{$Acap Bcap C$}
    end{pspicture}

    begin{pspicture}[shift=-4](0,-1)(5,4)
    arealIII
    arealV
    arealVI
    EndeEllipsen*{$Acap (Bcup C)$}
    end{pspicture}

    begin{pspicture}[shift=-4](0,-1)(5,4)
    arealI
    EreignisC*%
    EndeEllipsen*{$(overline{A}cap overline{B})cup C$}
    end{pspicture}

    begin{pspicture}[shift=-4](0,-1)(5,4)
    arealI
    arealIV
    arealVIII
    EndeEllipsen*{$overline{A}setminus (Bcap C)$}
    end{pspicture}

    begin{pspicture}[shift=-4](0,-1)(5,4)
    arealVIII
    EndeEllipsen*{$(overline{A}setminus B)cap C$}
    end{pspicture}

    begin{pspicture}[shift=-4](0,-1)(5,4)
    arealII
    arealV
    arealVI
    arealVII
    EndeEllipsen*{$(Asetminus B)cup (Bcap C)$}
    end{pspicture}

    begin{pspicture}[shift=-4](0,-1)(5,4)
    arealIII
    arealV
    EndeEllipsen*{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
    end{pspicture}


    end{document}




    Perhaps you want to check out this.



    documentclass[pstricks]{standalone}
    usepackage{pst-node}
    usepackage{xparse,xintexpr}

    %defradiusK{xinttheiexpr[6] 2*sqrt(3)/3relax}
    %
    %defKOEA{2.5,2}
    %defFOEA{radiusK,radiusK}
    %
    %defKOEB{2,1}
    %defFOEB{radiusK,radiusK}
    %
    %defKOEC{3,1}
    %defFOEC{radiusK,radiusK}
    %
    %defKOEO{2.5,1.375}
    %defFOEO{2.5,2.5}

    %uncomment the following lines to have ellipses
    defKOEA{1.9,2.2}
    defFOEA{1.4,1}

    defKOEB{3.3,2.2}
    defFOEB{1.2,1}

    defKOEC{2.75,1.4}
    defFOEC{1.4,1}

    defKOEO{2.5,2}
    defFOEO{2.5,2.0}

    NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
    IfBooleanTF{#1}{%
    psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
    psellipse(KOEA)(FOEA)}%
    }

    NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
    IfBooleanTF{#1}{%
    psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
    psellipse(KOEB)(FOEB)}%
    }

    NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
    IfBooleanTF{#1}{%
    psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
    psellipse(KOEC)(FOEC)}%
    }

    NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
    IfBooleanTF{#1}{%
    psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
    psellipse(KOEO)(FOEO)}%
    }

    NewDocumentCommand{EndeEllipsen}{sm}{%
    EreignisOmega%
    pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
    pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
    EreignisA
    EreignisB
    EreignisC
    rput[t](E){#2}%
    IfBooleanF{#1}{%
    rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
    rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
    rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
    rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
    }%
    }

    NewDocumentCommand{codeclip}{m}{%
    pscustom[linestyle=none]{%
    code{/clip /eoclip load def}%
    psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
    #1
    }%
    }

    NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    }%
    codeclip{%
    EreignisB
    }%
    codeclip{%
    EreignisC
    }%
    }%
    EreignisOmega*[#1][#2]%
    endpsclip
    }

    NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisB
    EreignisC
    }%
    codeclip{%
    EreignisC
    }%
    }%
    EreignisA*[#1][#2]%
    endpsclip
    }

    NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    EreignisB
    EreignisC
    }%
    codeclip{%
    EreignisC
    }%
    }%
    EreignisA*[#1][#2]%
    endpsclip
    }

    NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    EreignisC
    }%
    codeclip{%
    EreignisC
    }%
    }%
    EreignisB*[#1][#2]%
    endpsclip
    }

    NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    EreignisB
    EreignisC
    }%
    codeclip{%
    EreignisB
    }%
    }%
    EreignisA*[#1][#2]%
    endpsclip
    }

    NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
    psclip{EreignisB}
    psclip{EreignisC}%
    EreignisA*[#1][#2]%
    endpsclip
    endpsclip
    }

    NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    EreignisB
    EreignisC
    }%
    codeclip{%
    EreignisA
    }%
    }%
    EreignisC*[#1][#2]%
    endpsclip
    }

    NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    EreignisB
    }%
    codeclip{%
    EreignisB
    }%
    }%
    EreignisC*[#1][#2]%
    endpsclip
    }

    begin{document}


    begin{pspicture}[shift=-4](0,-1)(5,4)
    arealI
    EndeEllipsen{$Asetminus C$}
    end{pspicture}

    begin{pspicture}[shift=-4](0,-1)(5,4)
    arealVI
    EndeEllipsen{$Acap Bcap C$}
    end{pspicture}

    begin{pspicture}[shift=-4](0,-1)(5,4)
    arealIII
    arealV
    arealVI
    EndeEllipsen{$Acap (Bcup C)$}
    end{pspicture}

    begin{pspicture}[shift=-4](0,-1)(5,4)
    arealI
    EreignisC*%
    EndeEllipsen{$(overline{A}cap overline{B})cup C$}
    end{pspicture}

    begin{pspicture}[shift=-4](0,-1)(5,4)
    arealI
    arealIV
    arealVIII
    EndeEllipsen{$overline{A}setminus (Bcap C)$}
    end{pspicture}

    begin{pspicture}[shift=-4](0,-1)(5,4)
    arealVIII
    EndeEllipsen{$(overline{A}setminus B)cap C$}
    end{pspicture}

    begin{pspicture}[shift=-4](0,-1)(5,4)
    arealII
    arealV
    arealVI
    arealVII
    EndeEllipsen{$(Asetminus B)cup (Bcap C)$}
    end{pspicture}

    begin{pspicture}[shift=-4](0,-1)(5,4)
    arealIII
    arealV
    EndeEllipsen{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
    end{pspicture}


    end{document}




    With the help of xint-package using xintFor and xintForpair you can write



    VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%


    so every surface becomes an own color, or you write



    VennIII[blue](0.5){2,4,6,8}{Text}%


    and all becomes color blue with opacity 0.5.



    documentclass[pstricks]{standalone}
    usepackage{pst-node}
    usepackage{xparse,xintexpr}

    defKOEA{1.9,2.2}
    defFOEA{1.4,1}

    defKOEB{3.3,2.2}
    defFOEB{1.2,1}

    defKOEC{2.75,1.4}
    defFOEC{1.4,1}

    defKOEO{2.5,2}
    defFOEO{2.5,2.0}

    NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
    IfBooleanTF{#1}{%
    psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
    psellipse(KOEA)(FOEA)}%
    }

    NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
    IfBooleanTF{#1}{%
    psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
    psellipse(KOEB)(FOEB)}%
    }

    NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
    IfBooleanTF{#1}{%
    psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
    psellipse(KOEC)(FOEC)}%
    }

    NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
    IfBooleanTF{#1}{%
    psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
    psellipse(KOEO)(FOEO)}%
    }

    NewDocumentCommand{EndeEllipsen}{sm}{%
    EreignisOmega%
    pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
    pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
    EreignisA
    EreignisB
    EreignisC
    rput[t](E){#2}%
    IfBooleanF{#1}{%
    rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
    rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
    rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
    rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
    }%
    }

    NewDocumentCommand{codeclip}{m}{%
    pscustom[linestyle=none]{%
    code{/clip /eoclip load def}%
    psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
    #1
    }%
    }

    %ExplSyntaxOn
    NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    }%
    codeclip{%
    EreignisB
    }%
    codeclip{%
    EreignisC
    }%
    }%
    EreignisOmega*[#1][#2]%
    endpsclip
    }

    NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisB
    EreignisC
    }%
    codeclip{%
    EreignisC
    }%
    }%
    EreignisA*[#1][#2]%
    endpsclip
    }

    NewDocumentCommand{arealIII}{!O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    EreignisB
    EreignisC
    }%
    codeclip{%
    EreignisC
    }%
    }%
    EreignisA*[#1][#2]%
    endpsclip
    }

    NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    EreignisC
    }%
    codeclip{%
    EreignisC
    }%
    }%
    EreignisB*[#1][#2]%
    endpsclip
    }

    NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    EreignisB
    EreignisC
    }%
    codeclip{%
    EreignisB
    }%
    }%
    EreignisA*[#1][#2]%
    endpsclip
    }

    NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
    psclip{EreignisB}%
    psclip{EreignisC}%
    EreignisA*[#1][#2]%
    endpsclip
    endpsclip
    }

    NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    EreignisB
    EreignisC
    }%
    codeclip{%
    EreignisA
    }%
    }%
    EreignisC*[#1][#2]%
    endpsclip
    }

    NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
    psclip{%
    codeclip{%
    EreignisA
    EreignisB
    }%
    codeclip{%
    EreignisB
    }%
    }%
    EreignisC*[#1][#2]%
    endpsclip
    }
    %ExplSyntaxOff

    NewDocumentCommand{VIIIarea}{O{cyan}O{0.8}m}{%
    xintifboolexpr{#3=1}{arealI[#1][#2]}{}%
    xintifboolexpr{#3=2}{arealII[#1][#2]}{}%
    xintifboolexpr{#3=3}{arealIII[#1][#2]}{}%
    xintifboolexpr{#3=4}{arealIV[#1][#2]}{}%
    xintifboolexpr{#3=5}{arealV[#1][#2]}{}%
    xintifboolexpr{#3=6}{arealVI[#1][#2]}{}%
    xintifboolexpr{#3=7}{arealVII[#1][#2]}{}%
    xintifboolexpr{#3=8}{arealVIII[#1][#2]}{}%
    }

    NewDocumentCommand{VennIII}{oD(){0.8}m!g}{%
    IfValueTF{#1}%
    {%
    xintFor ##1 in {#3}do {VIIIarea[#1][#2]{##1}}%
    }%
    {%
    xintForpair ##1##2 in {#3}do {VIIIarea[##2][#2]{##1}}%
    }%
    EndeEllipsen{IfValueT{#4}{#4}}%
    }

    begin{document}

    begin{pspicture}(0,-1)(5,4)
    VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%
    end{pspicture}

    begin{pspicture}(0,-1)(5,4)
    VennIII[orange]{6}{$Acap Bcap C$}%
    end{pspicture}

    begin{pspicture}(0,-1)(5,4)
    VennIII[cyan]{3,5,6}{$Acap (Bcup C)$}
    end{pspicture}

    begin{pspicture}(0,-1)(5,4)
    VennIII[magenta](0.5){1,5,6,7}{$(overline{A}cap overline{B})cup C$}
    end{pspicture}

    begin{pspicture}(0,-1)(5,4)
    VennIII[green](0.2){1,4,8}{$overline{A}setminus (Bcap C)$}
    end{pspicture}

    begin{pspicture}(0,-1)(5,4)
    VennIII[cyan]{8}{$(overline{A}setminus B)cap C$}
    end{pspicture}

    begin{pspicture}(0,-1)(5,4)
    VennIII(1){(2,cyan),(5,orange),(6,green),(7,magenta)}{$(Asetminus B)cup (Bcap C)$}
    end{pspicture}

    begin{pspicture}(0,-1)(5,4)
    VennIII[cyan]{3,5}{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
    end{pspicture}


    end{document}


    enter image description here






    share|improve this answer























    • Hey bro, is there a shorter way? Your code seem being enormously complex.
      – chishimotoji
      Dec 1 at 10:48










    • This is because I first create all sorts of single surfaces by clipping. Then you can get any desired combination by fading in this area. This is a bit dull, but much easier to use. For example for area 2, area 4 and area 8you can use begin{pspicture}[shift=-4](0,-1)(5,4) arealI arealIV arealVIII EndeEllipsen{$overline{A}setminus (Bcap C)$} end{pspicture}
      – Thomas
      Dec 1 at 13:45













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    5 Answers
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    5 Answers
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    19














    A PSTricks solution just for fun!



    Answer 1



    documentclass[pstricks]{standalone}
    begin{document}
    begin{pspicture}(-5,-5)(5,5)
    pscustom[fillstyle=eofill,fillcolor=blue]
    {
    pscircle(1.5;90){3}
    pscircle(1.5;-30){3}
    pscircle(1.5;210){3}
    }
    end{pspicture}
    end{document}


    enter image description here



    The stroke color is left black just for a trivial reason.



    Cartesian coordinates are used in response to the request.



    documentclass[pstricks]{standalone}
    begin{document}
    begin{pspicture}(-5,-5)(5,5)
    pscustom[fillstyle=eofill,fillcolor=blue]
    {
    pscircle(0,1.5){3}
    pscircle(1.29,-0.75){3}
    pscircle(-1.29,-0.75){3}
    }
    end{pspicture}
    end{document}


    Answer 2



    Non-zero winding rule:



    documentclass[pstricks,border=12pt]{standalone}
    begin{document}
    begin{pspicture}[showgrid=t](-3,-3)(3,3)
    pscustom[fillstyle=solid,fillcolor=red]
    {
    pscircle{1}
    pscircle{2}
    }
    end{pspicture}
    end{document}


    enter image description here



    Non-zero winding rule:



    documentclass[pstricks,border=12pt]{standalone}
    begin{document}
    begin{pspicture}[showgrid=t](-3,-3)(3,3)
    pscustom[fillstyle=solid,fillcolor=red]
    {
    psarcn(0,0){1}{360}{0}
    pscircle{2}
    }
    end{pspicture}
    end{document}


    enter image description here



    Even-odd rule:



    documentclass[pstricks,border=12pt]{standalone}
    begin{document}
    begin{pspicture}[showgrid=t](-3,-3)(3,3)
    pscustom[fillstyle=eofill,fillcolor=red]
    {
    pscircle{1}
    pscircle{2}
    }
    end{pspicture}
    end{document}


    enter image description here






    share|improve this answer




























      19














      A PSTricks solution just for fun!



      Answer 1



      documentclass[pstricks]{standalone}
      begin{document}
      begin{pspicture}(-5,-5)(5,5)
      pscustom[fillstyle=eofill,fillcolor=blue]
      {
      pscircle(1.5;90){3}
      pscircle(1.5;-30){3}
      pscircle(1.5;210){3}
      }
      end{pspicture}
      end{document}


      enter image description here



      The stroke color is left black just for a trivial reason.



      Cartesian coordinates are used in response to the request.



      documentclass[pstricks]{standalone}
      begin{document}
      begin{pspicture}(-5,-5)(5,5)
      pscustom[fillstyle=eofill,fillcolor=blue]
      {
      pscircle(0,1.5){3}
      pscircle(1.29,-0.75){3}
      pscircle(-1.29,-0.75){3}
      }
      end{pspicture}
      end{document}


      Answer 2



      Non-zero winding rule:



      documentclass[pstricks,border=12pt]{standalone}
      begin{document}
      begin{pspicture}[showgrid=t](-3,-3)(3,3)
      pscustom[fillstyle=solid,fillcolor=red]
      {
      pscircle{1}
      pscircle{2}
      }
      end{pspicture}
      end{document}


      enter image description here



      Non-zero winding rule:



      documentclass[pstricks,border=12pt]{standalone}
      begin{document}
      begin{pspicture}[showgrid=t](-3,-3)(3,3)
      pscustom[fillstyle=solid,fillcolor=red]
      {
      psarcn(0,0){1}{360}{0}
      pscircle{2}
      }
      end{pspicture}
      end{document}


      enter image description here



      Even-odd rule:



      documentclass[pstricks,border=12pt]{standalone}
      begin{document}
      begin{pspicture}[showgrid=t](-3,-3)(3,3)
      pscustom[fillstyle=eofill,fillcolor=red]
      {
      pscircle{1}
      pscircle{2}
      }
      end{pspicture}
      end{document}


      enter image description here






      share|improve this answer


























        19












        19








        19






        A PSTricks solution just for fun!



        Answer 1



        documentclass[pstricks]{standalone}
        begin{document}
        begin{pspicture}(-5,-5)(5,5)
        pscustom[fillstyle=eofill,fillcolor=blue]
        {
        pscircle(1.5;90){3}
        pscircle(1.5;-30){3}
        pscircle(1.5;210){3}
        }
        end{pspicture}
        end{document}


        enter image description here



        The stroke color is left black just for a trivial reason.



        Cartesian coordinates are used in response to the request.



        documentclass[pstricks]{standalone}
        begin{document}
        begin{pspicture}(-5,-5)(5,5)
        pscustom[fillstyle=eofill,fillcolor=blue]
        {
        pscircle(0,1.5){3}
        pscircle(1.29,-0.75){3}
        pscircle(-1.29,-0.75){3}
        }
        end{pspicture}
        end{document}


        Answer 2



        Non-zero winding rule:



        documentclass[pstricks,border=12pt]{standalone}
        begin{document}
        begin{pspicture}[showgrid=t](-3,-3)(3,3)
        pscustom[fillstyle=solid,fillcolor=red]
        {
        pscircle{1}
        pscircle{2}
        }
        end{pspicture}
        end{document}


        enter image description here



        Non-zero winding rule:



        documentclass[pstricks,border=12pt]{standalone}
        begin{document}
        begin{pspicture}[showgrid=t](-3,-3)(3,3)
        pscustom[fillstyle=solid,fillcolor=red]
        {
        psarcn(0,0){1}{360}{0}
        pscircle{2}
        }
        end{pspicture}
        end{document}


        enter image description here



        Even-odd rule:



        documentclass[pstricks,border=12pt]{standalone}
        begin{document}
        begin{pspicture}[showgrid=t](-3,-3)(3,3)
        pscustom[fillstyle=eofill,fillcolor=red]
        {
        pscircle{1}
        pscircle{2}
        }
        end{pspicture}
        end{document}


        enter image description here






        share|improve this answer














        A PSTricks solution just for fun!



        Answer 1



        documentclass[pstricks]{standalone}
        begin{document}
        begin{pspicture}(-5,-5)(5,5)
        pscustom[fillstyle=eofill,fillcolor=blue]
        {
        pscircle(1.5;90){3}
        pscircle(1.5;-30){3}
        pscircle(1.5;210){3}
        }
        end{pspicture}
        end{document}


        enter image description here



        The stroke color is left black just for a trivial reason.



        Cartesian coordinates are used in response to the request.



        documentclass[pstricks]{standalone}
        begin{document}
        begin{pspicture}(-5,-5)(5,5)
        pscustom[fillstyle=eofill,fillcolor=blue]
        {
        pscircle(0,1.5){3}
        pscircle(1.29,-0.75){3}
        pscircle(-1.29,-0.75){3}
        }
        end{pspicture}
        end{document}


        Answer 2



        Non-zero winding rule:



        documentclass[pstricks,border=12pt]{standalone}
        begin{document}
        begin{pspicture}[showgrid=t](-3,-3)(3,3)
        pscustom[fillstyle=solid,fillcolor=red]
        {
        pscircle{1}
        pscircle{2}
        }
        end{pspicture}
        end{document}


        enter image description here



        Non-zero winding rule:



        documentclass[pstricks,border=12pt]{standalone}
        begin{document}
        begin{pspicture}[showgrid=t](-3,-3)(3,3)
        pscustom[fillstyle=solid,fillcolor=red]
        {
        psarcn(0,0){1}{360}{0}
        pscircle{2}
        }
        end{pspicture}
        end{document}


        enter image description here



        Even-odd rule:



        documentclass[pstricks,border=12pt]{standalone}
        begin{document}
        begin{pspicture}[showgrid=t](-3,-3)(3,3)
        pscustom[fillstyle=eofill,fillcolor=red]
        {
        pscircle{1}
        pscircle{2}
        }
        end{pspicture}
        end{document}


        enter image description here







        share|improve this answer














        share|improve this answer



        share|improve this answer








        edited Nov 30 at 9:06

























        answered Nov 30 at 7:59









        God Must Be Crazy

        5,60511039




        5,60511039























            16





            +500









            Here is an answer based on the one by @Thomas. Differences




            • the "elementary" regions I, II, ..., VIII are not numbered the same. My numbering is that "N" is the Roman number of "n+1" where "n" in binary is "abc", and the region is intersection of A or not A with B or not B with C or not C according to a, b, c = 0 or 1. (Boolean logic)


            • the macro needs only one input: a TeX formula for the set. Please enrich the syntax by adding suitable definitions converting TeX math macros into Boolean logic notation, as understood by xintexpr


            • I have dropped all fancy customization of colors, but xparse virtuosos will add the fancy optional arguments to re-install it if needed.



            Thus, the big point here is that xintexpr computes automatically from the TeX typesetting formula which regions are to be filled in diagram.




            attention to setminus it must be used either with parentheses setminus (...) or without but then with only one letter setminus A
            ok, setminus Acap B not ok, because the translation here to xintexpr
            boolean will do naively something equivalent to and not(A) and B, not the expected and not(A and B). In short, you must treat setminus as having maximally tying precedence.




            documentclass[pstricks, border=10pt]{standalone}
            usepackage{pst-node}
            usepackage{xparse,xintexpr}

            defKOEA{1.9,2.2}
            defFOEA{1.4,1}

            defKOEB{3.3,2.2}
            defFOEB{1.2,1}

            defKOEC{2.75,1.4}
            defFOEC{1.4,1}

            defKOEO{2.5,2}
            defFOEO{2.5,2.0}

            NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
            psellipse(KOEA)(FOEA)}%
            }

            NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
            psellipse(KOEB)(FOEB)}%
            }

            NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
            psellipse(KOEC)(FOEC)}%
            }

            NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
            psellipse(KOEO)(FOEO)}%
            }

            NewDocumentCommand{EndeEllipsen}{sm}{%
            EreignisOmega%
            pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
            pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
            EreignisA
            EreignisB
            EreignisC
            rput[t](E){#2}%
            IfBooleanF{#1}{%
            rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
            rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
            rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
            rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
            }%
            }

            NewDocumentCommand{codeclip}{m}{%
            pscustom[linestyle=none]{%
            code{/clip /eoclip load def}%
            psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
            #1
            }%
            }

            %ExplSyntaxOn
            % We could use some automated macro creation but well
            % 000
            NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisOmega*[#1][#2]%
            endpsclip
            }%
            % 001
            NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }
            % 010
            NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisB*[#1][#2]%
            endpsclip
            }
            % 011
            NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisA
            }%
            }%
            EreignisB*[#1][#2]%
            EreignisC*[#1][#2]%
            endpsclip
            }
            % 100
            NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }
            % 101
            NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisC
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisA*[#1][#2]%
            EreignisC*[#1][#2]%
            endpsclip
            }
            % 110
            NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            EreignisB*[#1][#2]%
            endpsclip
            }
            % 111
            NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            }%
            codeclip{%
            EreignisA
            EreignisC
            }%
            codeclip{%
            EreignisB
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            EreignisB*[#1][#2]%
            EreignisC*[#1][#2]%
            endpsclip
            }
            %ExplSyntaxOff

            %xintverbosetrue
            makeatletter
            newcommandVennFromTeX[1]{%
            VennFromTeX@main #1%
            }%
            defVennFromTeX@main$#1${%
            begingroup
            xintglobaldefstrue
            defoverline##1{!(##1)}% or not(##1)
            defcap{&&}% or 'and'
            defcup{||}% or 'or'
            defoplus{ 'xor' }%
            defsetminus##1{ifx(##1&&!(else &&!(##1)fi}%
            letbiglempty
            letbigrempty
            % ....
            % (add above all needed extra definitions: letBiglempty etc...)
            xintdeffunc MyBool(A, B, C) := #1;% #1 must use A, B, C only
            endgroup
            % we could make a loop here (using @Roman), but let's stay simple
            % I trust xparse experts can wrap this up in macros allowing to customize
            % the colors
            % ATTENTION THAT THESE arealI...VIII ARE NOT THE SAME AS IN @THOMAS ANSWER
            xintifboolexpr{MyBool(0, 0, 0)}{arealI[cyan][0.8]}{}%
            xintifboolexpr{MyBool(0, 0, 1)}{arealII[cyan][0.8]}{}%
            xintifboolexpr{MyBool(0, 1, 0)}{arealIII[cyan][0.8]}{}%
            xintifboolexpr{MyBool(0, 1, 1)}{arealIV[cyan][0.8]}{}%
            xintifboolexpr{MyBool(1, 0, 0)}{arealV[cyan][0.8]}{}%
            xintifboolexpr{MyBool(1, 0, 1)}{arealVI[cyan][0.8]}{}%
            xintifboolexpr{MyBool(1, 1, 0)}{arealVII[cyan][0.8]}{}%
            xintifboolexpr{MyBool(1, 1, 1)}{arealVIII[cyan][0.8]}{}%
            EndeEllipsen{$#1$}%
            }%
            makeatother

            begin{document}

            %testing if I, II, ..., VIII are as expected
            % makeatletter
            % xintFor*#1in{xintSeq{0}{7}}do{%
            % begin{pspicture}(0,-1)(5,4)
            % rput(2,0){thenumexpr1+#1}
            % @nameuse{areal@Roman{numexpr1+#1}}[cyan][0.8]
            % EndeEllipsen{}
            % end{pspicture}
            % }%
            % end{document}


            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$Acap Bcap C$}%
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$Acap (Bcup C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$(overline{A}cap overline{B})cup C$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$overline{A}setminus (Bcap C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$(overline{A}setminus B)cap C$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$(Asetminus B)cup (Bcap C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$Aoplus Boplus C$}
            end{pspicture}

            end{document}


            Produces



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here







            Here is code to generate all 256 Venn diagrams. Just insert it in body of above document and don't forget to add usepackage{xintbinhex} to preamble.



            % generating all graphics

            % 0<= n <= 255 has eight binary digits
            % abcdefgh
            % a=1 -> region VIII is included (A cap B cap C)
            % b=1 -> region VII is included
            % ...
            % h=1 -> region I is included (overline{A}cap overline{B} cap overline{C})
            % We want also to describe the region as a formula...
            % We could use 8 xintFor loops #1, ..., #8, but then
            % we still need to convert #1*7 to binary, #2*6, #3*5 etc...
            % I thus use xintbinhex per convenience but ifodd would be enough
            % As I use xintbinhex, I also use a single xintFor* loop

            %defgobbleone#1{}%
            defgobbletwo#1#2{}%
            xintFor* #1 in {xintSeq{0}{255}}:
            {%
            xintDigitsOfxintDecToBin{thenumexpr256+#1relax}toRegions
            % due to leading 1 there will be a shift of indexing in Regions
            edefx{xintifboolexpr{Regions{thenumexpr9-0}}% 000
            {unexpanded{allowbreakcup
            overline{A}capoverline{B}capoverline{C}}}%
            {}%
            xintifboolexpr{Regions{9-1}}% 001
            {unexpanded{allowbreakcup overline{A}capoverline{B}cap C}}%
            {}%
            xintifboolexpr{Regions{9-2}}% 010
            {unexpanded{allowbreakcup overline{A}cap B capoverline{C}}}%
            {}%
            xintifboolexpr{Regions{9-3}}% 011
            {unexpanded{allowbreakcup overline{A} cap B cap C}}%
            {}%
            xintifboolexpr{Regions{9-4}}% 100
            {unexpanded{allowbreakcup Acap overline{B}cap overline{C}}}%
            {}%
            xintifboolexpr{Regions{9-5}}% 101
            {unexpanded{allowbreakcup Acap overline{B}cap C}}%
            {}%
            xintifboolexpr{Regions{9-6}}% 110
            {unexpanded{allowbreakcup Acap Bcap overline{C}}}%
            {}%
            xintifboolexpr{Regions{9-7}}% 111
            {unexpanded{allowbreakcup Acap B cap C}}%
            {}%
            }%
            xintifForFirst{defx{emptyset}}
            {oodefx{expandaftergobbletwox}}%
            begin{pspicture}(0,-2)(5,4)
            % I will leave here each Region as individual call, so a color can
            % be added by modifying this code
            xintifboolexpr{Regions{9-0}}{arealI[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-1}}{arealII[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-2}}{arealIII[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-3}}{arealIV[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-4}}{arealV[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-5}}{arealVI[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-6}}{arealVII[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-7}}{arealVIII[cyan][0.8]}{}%
            EndeEllipsen{parbox{4cm}{centering$x$}}%
            end{pspicture}%
            }%


            Defect: the description of the set is as a disjoint union of atomic events. There might be some canonical shorter description but I never really thought about it. For example one of those diagram will represent $Omegasetminus A$ but this not the way it will be legended.



            Here is how this example comes out (on page 16 of document with nothing else, i.e. it corresponds to #1 = 15 in the loop, 15=1111 means to keep atomic events 0=000, 1=001, 2=010, 3=011, which is complement of A in Omega.



            enter image description here







            Here is now with 4 sets.



            This time, with TikZ code (I know neither PSTricks nor TikZ and can only survive from copying pre-existing drawing instructions; in this case I started from https://tex.stackexchange.com/a/100091/4686 by @JohnHammersley in 2013).



            First I include an image of all atomic events, which are the regions to which the Atomic... macros in code next refer. (this was done for checking while preparing answer)



            enter image description here



            Here is the code for VennFromTeX, use it as VennFromTeX{$ set formula with A, B, C, D $}. Same instructions as above for three sets.
            (one may wish to enlarge the syntax for example by allowing use of U or Omega and defining it in xintexpr to be simply 1, and similarly emptyset could be defined to be 0).



            documentclass[12pt, tikz, border=10pt]{standalone}

            usepackage{tikz}

            usetikzlibrary{positioning,shapes.geometric}

            usepackage{xintexpr}% for VennFromTeX


            % For drawing
            deffirstellip{(-1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
            defsecondellip{(-0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
            defthirdellip{(0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}
            deffourthellip{(1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}

            defbounding{(-5,-3) rectangle (5,4)}

            % Elementary sets
            % ABCD
            % abcd a, b, c, d in {0, 1}
            defAtomic{% 0000
            begin{scope}[even odd rule]% exterior
            clip firstellip (-5,-5) rectangle (5,5);
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] bounding;
            end{scope}
            }%
            defAtomici{% 0001
            begin{scope}[even odd rule]% fourth ellipse corner
            clip firstellip (-5,-5) rectangle (5,5);
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            fill[yellow] fourthellip;
            end{scope}
            }%
            defAtomicii{% 0010
            begin{scope}[even odd rule]% third ellipse corner
            clip firstellip (-5,-5) rectangle (5,5);
            clip secondellip (-5,-5) rectangle (5,5);
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] thirdellip;
            end{scope}
            }%
            defAtomiciii{% 0011
            begin{scope}[even odd rule]%
            clip firstellip (-5,-5) rectangle (5,5);
            clip secondellip (-5,-5) rectangle (5,5);
            clip fourthellip;
            fill[yellow] thirdellip;
            end{scope}
            }%
            defAtomiciv{% 0100
            begin{scope}[even odd rule]% second ellipse corner
            clip firstellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] secondellip;
            end{scope}
            }%
            defAtomicv{% 0101
            begin{scope}[even odd rule]%
            clip firstellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip;
            fill[yellow] secondellip;
            end{scope}
            }%
            defAtomicvi{% 0110
            begin{scope}[even odd rule]%
            clip firstellip (-5,-5) rectangle (5,5);
            clip thirdellip;
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] secondellip;
            end{scope}
            }%
            defAtomicvii{% 0111
            begin{scope}[even odd rule]%
            clip firstellip (-5,-5) rectangle (5,5);
            clip thirdellip;
            clip fourthellip;
            fill[yellow] secondellip;
            end{scope}
            }%
            defAtomicviii{% 1000
            begin{scope}[even odd rule]%
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicix{% 1001
            begin{scope}[even odd rule]%
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip;
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicx{% 1010
            begin{scope}[even odd rule]%
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip;
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicxi{% 1011
            begin{scope}[even odd rule]%
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip;
            clip fourthellip;
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicxii{% 1100
            begin{scope}[even odd rule]%
            clip secondellip;
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicxiii{% 1101
            begin{scope}[even odd rule]%
            clip secondellip;
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip;
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicxiv{% 1110
            begin{scope}[even odd rule]%
            clip secondellip;
            clip thirdellip;
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicxv{% 1111
            begin{scope}[even odd rule]%
            clip secondellip;
            clip thirdellip;
            clip fourthellip;
            fill[yellow] firstellip;
            end{scope}
            }%

            makeatletter
            newcommandVennFromTeX[1]{VennFromTeX@main #1}%

            defVennFromTeX@main$#1${%
            begingroup
            xintglobaldefstrue
            defoverline##1{!(##1)}% or not(##1)
            defcap{&&}% or 'and'
            defcup{||}% or 'or'
            defoplus{ 'xor' }%
            defsetminus##1{ifx(##1&&!(else &&!(##1)fi}%
            letbiglempty
            letbigrempty
            % ....
            % (add above all needed extra definitions: letBiglempty etc...)
            xintdeffunc MyBool(A, B, C, D) := #1;% #1 must use A, B, C, Donly
            endgroup
            begin{tikzpicture}

            xintFor* ##1 in {01}:
            {%
            xintFor* ##2 in {01}:
            {%
            xintFor* ##3 in {01}:
            {%
            xintFor* ##4 in {01}:
            {%
            xintifboolexpr{MyBool(##1, ##2, ##3, ##4)}
            {csname
            Atomicromannumeralnumexpr##1*8+##2*4+##3*2+##4endcsname}%
            {}%
            }%
            }%
            }%
            }%
            draw bounding;

            % fill[white] firstellip;
            % fill[white] secondellip;
            % fill[white] thirdellip;
            % fill[white] fourthellip;

            draw firstellip node [label={[xshift=-2cm, yshift=-0.9cm]$A$}] {};
            draw secondellip node [label={[xshift=-2.1cm, yshift=2.1cm]$B$}] {};
            draw thirdellip node [label={[xshift=2.1cm, yshift=2.1cm]$C$}] {};
            draw fourthellip node [label={[xshift=2cm, yshift=-0.9cm]$D$}] {};

            draw bounding node [label=below left:$U$] {};

            draw (0, 0) node [yshift=+4.4cm] {$#1$};

            end{tikzpicture}
            }%
            makeatother
            begin{document}

            % xintverbosetrue

            VennFromTeX{$Acap Bcap Ccap D$}

            VennFromTeX{$(Acap B)cup (Ccap D)$}

            VennFromTeX{$(overline{A}cupoverline{B})cap(overline{C}cupoverline{D})$}

            % attention to use parentheses for disambiguating setminus

            VennFromTeX{$(Acup B cup C) setminus(Bcup Ccup D)$}

            VennFromTeX{$(Acup B cup C) cap (Bcup Ccup D)$}

            VennFromTeX{$((Asetminus (Bcup Ccup D)) cup Bcap Ccap
            D)setminus (Acap Bcap Ccap D)$}

            end{document}


            Be careful to read the caveat top regarding usage of setminus in input.



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            and finally



            enter image description here






            share|improve this answer























            • (+1) Thank you for your answer!
              – chishimotoji
              Dec 2 at 11:27










            • (+1) Wow, fantastic!
              – Thomas
              Dec 2 at 11:34






            • 1




              Encyclopedic answer
              – Diaa
              Dec 2 at 11:38










            • careful in first part of answer when inputting a long formula that it some parts may be cut off the page, check the parbox in second part how to work around that, and I also increased the vertical dimension.
              – jfbu
              Dec 2 at 12:46






            • 2




              @ArtificialStupidity I have to get dinner but just give me time to learn PSTricks and I can do with 4 sets afterwards...
              – jfbu
              Dec 2 at 18:39
















            16





            +500









            Here is an answer based on the one by @Thomas. Differences




            • the "elementary" regions I, II, ..., VIII are not numbered the same. My numbering is that "N" is the Roman number of "n+1" where "n" in binary is "abc", and the region is intersection of A or not A with B or not B with C or not C according to a, b, c = 0 or 1. (Boolean logic)


            • the macro needs only one input: a TeX formula for the set. Please enrich the syntax by adding suitable definitions converting TeX math macros into Boolean logic notation, as understood by xintexpr


            • I have dropped all fancy customization of colors, but xparse virtuosos will add the fancy optional arguments to re-install it if needed.



            Thus, the big point here is that xintexpr computes automatically from the TeX typesetting formula which regions are to be filled in diagram.




            attention to setminus it must be used either with parentheses setminus (...) or without but then with only one letter setminus A
            ok, setminus Acap B not ok, because the translation here to xintexpr
            boolean will do naively something equivalent to and not(A) and B, not the expected and not(A and B). In short, you must treat setminus as having maximally tying precedence.




            documentclass[pstricks, border=10pt]{standalone}
            usepackage{pst-node}
            usepackage{xparse,xintexpr}

            defKOEA{1.9,2.2}
            defFOEA{1.4,1}

            defKOEB{3.3,2.2}
            defFOEB{1.2,1}

            defKOEC{2.75,1.4}
            defFOEC{1.4,1}

            defKOEO{2.5,2}
            defFOEO{2.5,2.0}

            NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
            psellipse(KOEA)(FOEA)}%
            }

            NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
            psellipse(KOEB)(FOEB)}%
            }

            NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
            psellipse(KOEC)(FOEC)}%
            }

            NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
            psellipse(KOEO)(FOEO)}%
            }

            NewDocumentCommand{EndeEllipsen}{sm}{%
            EreignisOmega%
            pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
            pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
            EreignisA
            EreignisB
            EreignisC
            rput[t](E){#2}%
            IfBooleanF{#1}{%
            rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
            rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
            rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
            rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
            }%
            }

            NewDocumentCommand{codeclip}{m}{%
            pscustom[linestyle=none]{%
            code{/clip /eoclip load def}%
            psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
            #1
            }%
            }

            %ExplSyntaxOn
            % We could use some automated macro creation but well
            % 000
            NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisOmega*[#1][#2]%
            endpsclip
            }%
            % 001
            NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }
            % 010
            NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisB*[#1][#2]%
            endpsclip
            }
            % 011
            NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisA
            }%
            }%
            EreignisB*[#1][#2]%
            EreignisC*[#1][#2]%
            endpsclip
            }
            % 100
            NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }
            % 101
            NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisC
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisA*[#1][#2]%
            EreignisC*[#1][#2]%
            endpsclip
            }
            % 110
            NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            EreignisB*[#1][#2]%
            endpsclip
            }
            % 111
            NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            }%
            codeclip{%
            EreignisA
            EreignisC
            }%
            codeclip{%
            EreignisB
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            EreignisB*[#1][#2]%
            EreignisC*[#1][#2]%
            endpsclip
            }
            %ExplSyntaxOff

            %xintverbosetrue
            makeatletter
            newcommandVennFromTeX[1]{%
            VennFromTeX@main #1%
            }%
            defVennFromTeX@main$#1${%
            begingroup
            xintglobaldefstrue
            defoverline##1{!(##1)}% or not(##1)
            defcap{&&}% or 'and'
            defcup{||}% or 'or'
            defoplus{ 'xor' }%
            defsetminus##1{ifx(##1&&!(else &&!(##1)fi}%
            letbiglempty
            letbigrempty
            % ....
            % (add above all needed extra definitions: letBiglempty etc...)
            xintdeffunc MyBool(A, B, C) := #1;% #1 must use A, B, C only
            endgroup
            % we could make a loop here (using @Roman), but let's stay simple
            % I trust xparse experts can wrap this up in macros allowing to customize
            % the colors
            % ATTENTION THAT THESE arealI...VIII ARE NOT THE SAME AS IN @THOMAS ANSWER
            xintifboolexpr{MyBool(0, 0, 0)}{arealI[cyan][0.8]}{}%
            xintifboolexpr{MyBool(0, 0, 1)}{arealII[cyan][0.8]}{}%
            xintifboolexpr{MyBool(0, 1, 0)}{arealIII[cyan][0.8]}{}%
            xintifboolexpr{MyBool(0, 1, 1)}{arealIV[cyan][0.8]}{}%
            xintifboolexpr{MyBool(1, 0, 0)}{arealV[cyan][0.8]}{}%
            xintifboolexpr{MyBool(1, 0, 1)}{arealVI[cyan][0.8]}{}%
            xintifboolexpr{MyBool(1, 1, 0)}{arealVII[cyan][0.8]}{}%
            xintifboolexpr{MyBool(1, 1, 1)}{arealVIII[cyan][0.8]}{}%
            EndeEllipsen{$#1$}%
            }%
            makeatother

            begin{document}

            %testing if I, II, ..., VIII are as expected
            % makeatletter
            % xintFor*#1in{xintSeq{0}{7}}do{%
            % begin{pspicture}(0,-1)(5,4)
            % rput(2,0){thenumexpr1+#1}
            % @nameuse{areal@Roman{numexpr1+#1}}[cyan][0.8]
            % EndeEllipsen{}
            % end{pspicture}
            % }%
            % end{document}


            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$Acap Bcap C$}%
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$Acap (Bcup C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$(overline{A}cap overline{B})cup C$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$overline{A}setminus (Bcap C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$(overline{A}setminus B)cap C$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$(Asetminus B)cup (Bcap C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$Aoplus Boplus C$}
            end{pspicture}

            end{document}


            Produces



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here







            Here is code to generate all 256 Venn diagrams. Just insert it in body of above document and don't forget to add usepackage{xintbinhex} to preamble.



            % generating all graphics

            % 0<= n <= 255 has eight binary digits
            % abcdefgh
            % a=1 -> region VIII is included (A cap B cap C)
            % b=1 -> region VII is included
            % ...
            % h=1 -> region I is included (overline{A}cap overline{B} cap overline{C})
            % We want also to describe the region as a formula...
            % We could use 8 xintFor loops #1, ..., #8, but then
            % we still need to convert #1*7 to binary, #2*6, #3*5 etc...
            % I thus use xintbinhex per convenience but ifodd would be enough
            % As I use xintbinhex, I also use a single xintFor* loop

            %defgobbleone#1{}%
            defgobbletwo#1#2{}%
            xintFor* #1 in {xintSeq{0}{255}}:
            {%
            xintDigitsOfxintDecToBin{thenumexpr256+#1relax}toRegions
            % due to leading 1 there will be a shift of indexing in Regions
            edefx{xintifboolexpr{Regions{thenumexpr9-0}}% 000
            {unexpanded{allowbreakcup
            overline{A}capoverline{B}capoverline{C}}}%
            {}%
            xintifboolexpr{Regions{9-1}}% 001
            {unexpanded{allowbreakcup overline{A}capoverline{B}cap C}}%
            {}%
            xintifboolexpr{Regions{9-2}}% 010
            {unexpanded{allowbreakcup overline{A}cap B capoverline{C}}}%
            {}%
            xintifboolexpr{Regions{9-3}}% 011
            {unexpanded{allowbreakcup overline{A} cap B cap C}}%
            {}%
            xintifboolexpr{Regions{9-4}}% 100
            {unexpanded{allowbreakcup Acap overline{B}cap overline{C}}}%
            {}%
            xintifboolexpr{Regions{9-5}}% 101
            {unexpanded{allowbreakcup Acap overline{B}cap C}}%
            {}%
            xintifboolexpr{Regions{9-6}}% 110
            {unexpanded{allowbreakcup Acap Bcap overline{C}}}%
            {}%
            xintifboolexpr{Regions{9-7}}% 111
            {unexpanded{allowbreakcup Acap B cap C}}%
            {}%
            }%
            xintifForFirst{defx{emptyset}}
            {oodefx{expandaftergobbletwox}}%
            begin{pspicture}(0,-2)(5,4)
            % I will leave here each Region as individual call, so a color can
            % be added by modifying this code
            xintifboolexpr{Regions{9-0}}{arealI[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-1}}{arealII[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-2}}{arealIII[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-3}}{arealIV[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-4}}{arealV[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-5}}{arealVI[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-6}}{arealVII[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-7}}{arealVIII[cyan][0.8]}{}%
            EndeEllipsen{parbox{4cm}{centering$x$}}%
            end{pspicture}%
            }%


            Defect: the description of the set is as a disjoint union of atomic events. There might be some canonical shorter description but I never really thought about it. For example one of those diagram will represent $Omegasetminus A$ but this not the way it will be legended.



            Here is how this example comes out (on page 16 of document with nothing else, i.e. it corresponds to #1 = 15 in the loop, 15=1111 means to keep atomic events 0=000, 1=001, 2=010, 3=011, which is complement of A in Omega.



            enter image description here







            Here is now with 4 sets.



            This time, with TikZ code (I know neither PSTricks nor TikZ and can only survive from copying pre-existing drawing instructions; in this case I started from https://tex.stackexchange.com/a/100091/4686 by @JohnHammersley in 2013).



            First I include an image of all atomic events, which are the regions to which the Atomic... macros in code next refer. (this was done for checking while preparing answer)



            enter image description here



            Here is the code for VennFromTeX, use it as VennFromTeX{$ set formula with A, B, C, D $}. Same instructions as above for three sets.
            (one may wish to enlarge the syntax for example by allowing use of U or Omega and defining it in xintexpr to be simply 1, and similarly emptyset could be defined to be 0).



            documentclass[12pt, tikz, border=10pt]{standalone}

            usepackage{tikz}

            usetikzlibrary{positioning,shapes.geometric}

            usepackage{xintexpr}% for VennFromTeX


            % For drawing
            deffirstellip{(-1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
            defsecondellip{(-0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
            defthirdellip{(0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}
            deffourthellip{(1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}

            defbounding{(-5,-3) rectangle (5,4)}

            % Elementary sets
            % ABCD
            % abcd a, b, c, d in {0, 1}
            defAtomic{% 0000
            begin{scope}[even odd rule]% exterior
            clip firstellip (-5,-5) rectangle (5,5);
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] bounding;
            end{scope}
            }%
            defAtomici{% 0001
            begin{scope}[even odd rule]% fourth ellipse corner
            clip firstellip (-5,-5) rectangle (5,5);
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            fill[yellow] fourthellip;
            end{scope}
            }%
            defAtomicii{% 0010
            begin{scope}[even odd rule]% third ellipse corner
            clip firstellip (-5,-5) rectangle (5,5);
            clip secondellip (-5,-5) rectangle (5,5);
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] thirdellip;
            end{scope}
            }%
            defAtomiciii{% 0011
            begin{scope}[even odd rule]%
            clip firstellip (-5,-5) rectangle (5,5);
            clip secondellip (-5,-5) rectangle (5,5);
            clip fourthellip;
            fill[yellow] thirdellip;
            end{scope}
            }%
            defAtomiciv{% 0100
            begin{scope}[even odd rule]% second ellipse corner
            clip firstellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] secondellip;
            end{scope}
            }%
            defAtomicv{% 0101
            begin{scope}[even odd rule]%
            clip firstellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip;
            fill[yellow] secondellip;
            end{scope}
            }%
            defAtomicvi{% 0110
            begin{scope}[even odd rule]%
            clip firstellip (-5,-5) rectangle (5,5);
            clip thirdellip;
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] secondellip;
            end{scope}
            }%
            defAtomicvii{% 0111
            begin{scope}[even odd rule]%
            clip firstellip (-5,-5) rectangle (5,5);
            clip thirdellip;
            clip fourthellip;
            fill[yellow] secondellip;
            end{scope}
            }%
            defAtomicviii{% 1000
            begin{scope}[even odd rule]%
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicix{% 1001
            begin{scope}[even odd rule]%
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip;
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicx{% 1010
            begin{scope}[even odd rule]%
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip;
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicxi{% 1011
            begin{scope}[even odd rule]%
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip;
            clip fourthellip;
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicxii{% 1100
            begin{scope}[even odd rule]%
            clip secondellip;
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicxiii{% 1101
            begin{scope}[even odd rule]%
            clip secondellip;
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip;
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicxiv{% 1110
            begin{scope}[even odd rule]%
            clip secondellip;
            clip thirdellip;
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicxv{% 1111
            begin{scope}[even odd rule]%
            clip secondellip;
            clip thirdellip;
            clip fourthellip;
            fill[yellow] firstellip;
            end{scope}
            }%

            makeatletter
            newcommandVennFromTeX[1]{VennFromTeX@main #1}%

            defVennFromTeX@main$#1${%
            begingroup
            xintglobaldefstrue
            defoverline##1{!(##1)}% or not(##1)
            defcap{&&}% or 'and'
            defcup{||}% or 'or'
            defoplus{ 'xor' }%
            defsetminus##1{ifx(##1&&!(else &&!(##1)fi}%
            letbiglempty
            letbigrempty
            % ....
            % (add above all needed extra definitions: letBiglempty etc...)
            xintdeffunc MyBool(A, B, C, D) := #1;% #1 must use A, B, C, Donly
            endgroup
            begin{tikzpicture}

            xintFor* ##1 in {01}:
            {%
            xintFor* ##2 in {01}:
            {%
            xintFor* ##3 in {01}:
            {%
            xintFor* ##4 in {01}:
            {%
            xintifboolexpr{MyBool(##1, ##2, ##3, ##4)}
            {csname
            Atomicromannumeralnumexpr##1*8+##2*4+##3*2+##4endcsname}%
            {}%
            }%
            }%
            }%
            }%
            draw bounding;

            % fill[white] firstellip;
            % fill[white] secondellip;
            % fill[white] thirdellip;
            % fill[white] fourthellip;

            draw firstellip node [label={[xshift=-2cm, yshift=-0.9cm]$A$}] {};
            draw secondellip node [label={[xshift=-2.1cm, yshift=2.1cm]$B$}] {};
            draw thirdellip node [label={[xshift=2.1cm, yshift=2.1cm]$C$}] {};
            draw fourthellip node [label={[xshift=2cm, yshift=-0.9cm]$D$}] {};

            draw bounding node [label=below left:$U$] {};

            draw (0, 0) node [yshift=+4.4cm] {$#1$};

            end{tikzpicture}
            }%
            makeatother
            begin{document}

            % xintverbosetrue

            VennFromTeX{$Acap Bcap Ccap D$}

            VennFromTeX{$(Acap B)cup (Ccap D)$}

            VennFromTeX{$(overline{A}cupoverline{B})cap(overline{C}cupoverline{D})$}

            % attention to use parentheses for disambiguating setminus

            VennFromTeX{$(Acup B cup C) setminus(Bcup Ccup D)$}

            VennFromTeX{$(Acup B cup C) cap (Bcup Ccup D)$}

            VennFromTeX{$((Asetminus (Bcup Ccup D)) cup Bcap Ccap
            D)setminus (Acap Bcap Ccap D)$}

            end{document}


            Be careful to read the caveat top regarding usage of setminus in input.



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            and finally



            enter image description here






            share|improve this answer























            • (+1) Thank you for your answer!
              – chishimotoji
              Dec 2 at 11:27










            • (+1) Wow, fantastic!
              – Thomas
              Dec 2 at 11:34






            • 1




              Encyclopedic answer
              – Diaa
              Dec 2 at 11:38










            • careful in first part of answer when inputting a long formula that it some parts may be cut off the page, check the parbox in second part how to work around that, and I also increased the vertical dimension.
              – jfbu
              Dec 2 at 12:46






            • 2




              @ArtificialStupidity I have to get dinner but just give me time to learn PSTricks and I can do with 4 sets afterwards...
              – jfbu
              Dec 2 at 18:39














            16





            +500







            16





            +500



            16




            +500




            Here is an answer based on the one by @Thomas. Differences




            • the "elementary" regions I, II, ..., VIII are not numbered the same. My numbering is that "N" is the Roman number of "n+1" where "n" in binary is "abc", and the region is intersection of A or not A with B or not B with C or not C according to a, b, c = 0 or 1. (Boolean logic)


            • the macro needs only one input: a TeX formula for the set. Please enrich the syntax by adding suitable definitions converting TeX math macros into Boolean logic notation, as understood by xintexpr


            • I have dropped all fancy customization of colors, but xparse virtuosos will add the fancy optional arguments to re-install it if needed.



            Thus, the big point here is that xintexpr computes automatically from the TeX typesetting formula which regions are to be filled in diagram.




            attention to setminus it must be used either with parentheses setminus (...) or without but then with only one letter setminus A
            ok, setminus Acap B not ok, because the translation here to xintexpr
            boolean will do naively something equivalent to and not(A) and B, not the expected and not(A and B). In short, you must treat setminus as having maximally tying precedence.




            documentclass[pstricks, border=10pt]{standalone}
            usepackage{pst-node}
            usepackage{xparse,xintexpr}

            defKOEA{1.9,2.2}
            defFOEA{1.4,1}

            defKOEB{3.3,2.2}
            defFOEB{1.2,1}

            defKOEC{2.75,1.4}
            defFOEC{1.4,1}

            defKOEO{2.5,2}
            defFOEO{2.5,2.0}

            NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
            psellipse(KOEA)(FOEA)}%
            }

            NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
            psellipse(KOEB)(FOEB)}%
            }

            NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
            psellipse(KOEC)(FOEC)}%
            }

            NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
            psellipse(KOEO)(FOEO)}%
            }

            NewDocumentCommand{EndeEllipsen}{sm}{%
            EreignisOmega%
            pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
            pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
            EreignisA
            EreignisB
            EreignisC
            rput[t](E){#2}%
            IfBooleanF{#1}{%
            rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
            rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
            rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
            rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
            }%
            }

            NewDocumentCommand{codeclip}{m}{%
            pscustom[linestyle=none]{%
            code{/clip /eoclip load def}%
            psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
            #1
            }%
            }

            %ExplSyntaxOn
            % We could use some automated macro creation but well
            % 000
            NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisOmega*[#1][#2]%
            endpsclip
            }%
            % 001
            NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }
            % 010
            NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisB*[#1][#2]%
            endpsclip
            }
            % 011
            NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisA
            }%
            }%
            EreignisB*[#1][#2]%
            EreignisC*[#1][#2]%
            endpsclip
            }
            % 100
            NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }
            % 101
            NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisC
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisA*[#1][#2]%
            EreignisC*[#1][#2]%
            endpsclip
            }
            % 110
            NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            EreignisB*[#1][#2]%
            endpsclip
            }
            % 111
            NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            }%
            codeclip{%
            EreignisA
            EreignisC
            }%
            codeclip{%
            EreignisB
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            EreignisB*[#1][#2]%
            EreignisC*[#1][#2]%
            endpsclip
            }
            %ExplSyntaxOff

            %xintverbosetrue
            makeatletter
            newcommandVennFromTeX[1]{%
            VennFromTeX@main #1%
            }%
            defVennFromTeX@main$#1${%
            begingroup
            xintglobaldefstrue
            defoverline##1{!(##1)}% or not(##1)
            defcap{&&}% or 'and'
            defcup{||}% or 'or'
            defoplus{ 'xor' }%
            defsetminus##1{ifx(##1&&!(else &&!(##1)fi}%
            letbiglempty
            letbigrempty
            % ....
            % (add above all needed extra definitions: letBiglempty etc...)
            xintdeffunc MyBool(A, B, C) := #1;% #1 must use A, B, C only
            endgroup
            % we could make a loop here (using @Roman), but let's stay simple
            % I trust xparse experts can wrap this up in macros allowing to customize
            % the colors
            % ATTENTION THAT THESE arealI...VIII ARE NOT THE SAME AS IN @THOMAS ANSWER
            xintifboolexpr{MyBool(0, 0, 0)}{arealI[cyan][0.8]}{}%
            xintifboolexpr{MyBool(0, 0, 1)}{arealII[cyan][0.8]}{}%
            xintifboolexpr{MyBool(0, 1, 0)}{arealIII[cyan][0.8]}{}%
            xintifboolexpr{MyBool(0, 1, 1)}{arealIV[cyan][0.8]}{}%
            xintifboolexpr{MyBool(1, 0, 0)}{arealV[cyan][0.8]}{}%
            xintifboolexpr{MyBool(1, 0, 1)}{arealVI[cyan][0.8]}{}%
            xintifboolexpr{MyBool(1, 1, 0)}{arealVII[cyan][0.8]}{}%
            xintifboolexpr{MyBool(1, 1, 1)}{arealVIII[cyan][0.8]}{}%
            EndeEllipsen{$#1$}%
            }%
            makeatother

            begin{document}

            %testing if I, II, ..., VIII are as expected
            % makeatletter
            % xintFor*#1in{xintSeq{0}{7}}do{%
            % begin{pspicture}(0,-1)(5,4)
            % rput(2,0){thenumexpr1+#1}
            % @nameuse{areal@Roman{numexpr1+#1}}[cyan][0.8]
            % EndeEllipsen{}
            % end{pspicture}
            % }%
            % end{document}


            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$Acap Bcap C$}%
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$Acap (Bcup C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$(overline{A}cap overline{B})cup C$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$overline{A}setminus (Bcap C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$(overline{A}setminus B)cap C$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$(Asetminus B)cup (Bcap C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$Aoplus Boplus C$}
            end{pspicture}

            end{document}


            Produces



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here







            Here is code to generate all 256 Venn diagrams. Just insert it in body of above document and don't forget to add usepackage{xintbinhex} to preamble.



            % generating all graphics

            % 0<= n <= 255 has eight binary digits
            % abcdefgh
            % a=1 -> region VIII is included (A cap B cap C)
            % b=1 -> region VII is included
            % ...
            % h=1 -> region I is included (overline{A}cap overline{B} cap overline{C})
            % We want also to describe the region as a formula...
            % We could use 8 xintFor loops #1, ..., #8, but then
            % we still need to convert #1*7 to binary, #2*6, #3*5 etc...
            % I thus use xintbinhex per convenience but ifodd would be enough
            % As I use xintbinhex, I also use a single xintFor* loop

            %defgobbleone#1{}%
            defgobbletwo#1#2{}%
            xintFor* #1 in {xintSeq{0}{255}}:
            {%
            xintDigitsOfxintDecToBin{thenumexpr256+#1relax}toRegions
            % due to leading 1 there will be a shift of indexing in Regions
            edefx{xintifboolexpr{Regions{thenumexpr9-0}}% 000
            {unexpanded{allowbreakcup
            overline{A}capoverline{B}capoverline{C}}}%
            {}%
            xintifboolexpr{Regions{9-1}}% 001
            {unexpanded{allowbreakcup overline{A}capoverline{B}cap C}}%
            {}%
            xintifboolexpr{Regions{9-2}}% 010
            {unexpanded{allowbreakcup overline{A}cap B capoverline{C}}}%
            {}%
            xintifboolexpr{Regions{9-3}}% 011
            {unexpanded{allowbreakcup overline{A} cap B cap C}}%
            {}%
            xintifboolexpr{Regions{9-4}}% 100
            {unexpanded{allowbreakcup Acap overline{B}cap overline{C}}}%
            {}%
            xintifboolexpr{Regions{9-5}}% 101
            {unexpanded{allowbreakcup Acap overline{B}cap C}}%
            {}%
            xintifboolexpr{Regions{9-6}}% 110
            {unexpanded{allowbreakcup Acap Bcap overline{C}}}%
            {}%
            xintifboolexpr{Regions{9-7}}% 111
            {unexpanded{allowbreakcup Acap B cap C}}%
            {}%
            }%
            xintifForFirst{defx{emptyset}}
            {oodefx{expandaftergobbletwox}}%
            begin{pspicture}(0,-2)(5,4)
            % I will leave here each Region as individual call, so a color can
            % be added by modifying this code
            xintifboolexpr{Regions{9-0}}{arealI[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-1}}{arealII[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-2}}{arealIII[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-3}}{arealIV[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-4}}{arealV[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-5}}{arealVI[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-6}}{arealVII[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-7}}{arealVIII[cyan][0.8]}{}%
            EndeEllipsen{parbox{4cm}{centering$x$}}%
            end{pspicture}%
            }%


            Defect: the description of the set is as a disjoint union of atomic events. There might be some canonical shorter description but I never really thought about it. For example one of those diagram will represent $Omegasetminus A$ but this not the way it will be legended.



            Here is how this example comes out (on page 16 of document with nothing else, i.e. it corresponds to #1 = 15 in the loop, 15=1111 means to keep atomic events 0=000, 1=001, 2=010, 3=011, which is complement of A in Omega.



            enter image description here







            Here is now with 4 sets.



            This time, with TikZ code (I know neither PSTricks nor TikZ and can only survive from copying pre-existing drawing instructions; in this case I started from https://tex.stackexchange.com/a/100091/4686 by @JohnHammersley in 2013).



            First I include an image of all atomic events, which are the regions to which the Atomic... macros in code next refer. (this was done for checking while preparing answer)



            enter image description here



            Here is the code for VennFromTeX, use it as VennFromTeX{$ set formula with A, B, C, D $}. Same instructions as above for three sets.
            (one may wish to enlarge the syntax for example by allowing use of U or Omega and defining it in xintexpr to be simply 1, and similarly emptyset could be defined to be 0).



            documentclass[12pt, tikz, border=10pt]{standalone}

            usepackage{tikz}

            usetikzlibrary{positioning,shapes.geometric}

            usepackage{xintexpr}% for VennFromTeX


            % For drawing
            deffirstellip{(-1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
            defsecondellip{(-0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
            defthirdellip{(0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}
            deffourthellip{(1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}

            defbounding{(-5,-3) rectangle (5,4)}

            % Elementary sets
            % ABCD
            % abcd a, b, c, d in {0, 1}
            defAtomic{% 0000
            begin{scope}[even odd rule]% exterior
            clip firstellip (-5,-5) rectangle (5,5);
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] bounding;
            end{scope}
            }%
            defAtomici{% 0001
            begin{scope}[even odd rule]% fourth ellipse corner
            clip firstellip (-5,-5) rectangle (5,5);
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            fill[yellow] fourthellip;
            end{scope}
            }%
            defAtomicii{% 0010
            begin{scope}[even odd rule]% third ellipse corner
            clip firstellip (-5,-5) rectangle (5,5);
            clip secondellip (-5,-5) rectangle (5,5);
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] thirdellip;
            end{scope}
            }%
            defAtomiciii{% 0011
            begin{scope}[even odd rule]%
            clip firstellip (-5,-5) rectangle (5,5);
            clip secondellip (-5,-5) rectangle (5,5);
            clip fourthellip;
            fill[yellow] thirdellip;
            end{scope}
            }%
            defAtomiciv{% 0100
            begin{scope}[even odd rule]% second ellipse corner
            clip firstellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] secondellip;
            end{scope}
            }%
            defAtomicv{% 0101
            begin{scope}[even odd rule]%
            clip firstellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip;
            fill[yellow] secondellip;
            end{scope}
            }%
            defAtomicvi{% 0110
            begin{scope}[even odd rule]%
            clip firstellip (-5,-5) rectangle (5,5);
            clip thirdellip;
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] secondellip;
            end{scope}
            }%
            defAtomicvii{% 0111
            begin{scope}[even odd rule]%
            clip firstellip (-5,-5) rectangle (5,5);
            clip thirdellip;
            clip fourthellip;
            fill[yellow] secondellip;
            end{scope}
            }%
            defAtomicviii{% 1000
            begin{scope}[even odd rule]%
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicix{% 1001
            begin{scope}[even odd rule]%
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip;
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicx{% 1010
            begin{scope}[even odd rule]%
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip;
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicxi{% 1011
            begin{scope}[even odd rule]%
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip;
            clip fourthellip;
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicxii{% 1100
            begin{scope}[even odd rule]%
            clip secondellip;
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicxiii{% 1101
            begin{scope}[even odd rule]%
            clip secondellip;
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip;
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicxiv{% 1110
            begin{scope}[even odd rule]%
            clip secondellip;
            clip thirdellip;
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicxv{% 1111
            begin{scope}[even odd rule]%
            clip secondellip;
            clip thirdellip;
            clip fourthellip;
            fill[yellow] firstellip;
            end{scope}
            }%

            makeatletter
            newcommandVennFromTeX[1]{VennFromTeX@main #1}%

            defVennFromTeX@main$#1${%
            begingroup
            xintglobaldefstrue
            defoverline##1{!(##1)}% or not(##1)
            defcap{&&}% or 'and'
            defcup{||}% or 'or'
            defoplus{ 'xor' }%
            defsetminus##1{ifx(##1&&!(else &&!(##1)fi}%
            letbiglempty
            letbigrempty
            % ....
            % (add above all needed extra definitions: letBiglempty etc...)
            xintdeffunc MyBool(A, B, C, D) := #1;% #1 must use A, B, C, Donly
            endgroup
            begin{tikzpicture}

            xintFor* ##1 in {01}:
            {%
            xintFor* ##2 in {01}:
            {%
            xintFor* ##3 in {01}:
            {%
            xintFor* ##4 in {01}:
            {%
            xintifboolexpr{MyBool(##1, ##2, ##3, ##4)}
            {csname
            Atomicromannumeralnumexpr##1*8+##2*4+##3*2+##4endcsname}%
            {}%
            }%
            }%
            }%
            }%
            draw bounding;

            % fill[white] firstellip;
            % fill[white] secondellip;
            % fill[white] thirdellip;
            % fill[white] fourthellip;

            draw firstellip node [label={[xshift=-2cm, yshift=-0.9cm]$A$}] {};
            draw secondellip node [label={[xshift=-2.1cm, yshift=2.1cm]$B$}] {};
            draw thirdellip node [label={[xshift=2.1cm, yshift=2.1cm]$C$}] {};
            draw fourthellip node [label={[xshift=2cm, yshift=-0.9cm]$D$}] {};

            draw bounding node [label=below left:$U$] {};

            draw (0, 0) node [yshift=+4.4cm] {$#1$};

            end{tikzpicture}
            }%
            makeatother
            begin{document}

            % xintverbosetrue

            VennFromTeX{$Acap Bcap Ccap D$}

            VennFromTeX{$(Acap B)cup (Ccap D)$}

            VennFromTeX{$(overline{A}cupoverline{B})cap(overline{C}cupoverline{D})$}

            % attention to use parentheses for disambiguating setminus

            VennFromTeX{$(Acup B cup C) setminus(Bcup Ccup D)$}

            VennFromTeX{$(Acup B cup C) cap (Bcup Ccup D)$}

            VennFromTeX{$((Asetminus (Bcup Ccup D)) cup Bcap Ccap
            D)setminus (Acap Bcap Ccap D)$}

            end{document}


            Be careful to read the caveat top regarding usage of setminus in input.



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            and finally



            enter image description here






            share|improve this answer














            Here is an answer based on the one by @Thomas. Differences




            • the "elementary" regions I, II, ..., VIII are not numbered the same. My numbering is that "N" is the Roman number of "n+1" where "n" in binary is "abc", and the region is intersection of A or not A with B or not B with C or not C according to a, b, c = 0 or 1. (Boolean logic)


            • the macro needs only one input: a TeX formula for the set. Please enrich the syntax by adding suitable definitions converting TeX math macros into Boolean logic notation, as understood by xintexpr


            • I have dropped all fancy customization of colors, but xparse virtuosos will add the fancy optional arguments to re-install it if needed.



            Thus, the big point here is that xintexpr computes automatically from the TeX typesetting formula which regions are to be filled in diagram.




            attention to setminus it must be used either with parentheses setminus (...) or without but then with only one letter setminus A
            ok, setminus Acap B not ok, because the translation here to xintexpr
            boolean will do naively something equivalent to and not(A) and B, not the expected and not(A and B). In short, you must treat setminus as having maximally tying precedence.




            documentclass[pstricks, border=10pt]{standalone}
            usepackage{pst-node}
            usepackage{xparse,xintexpr}

            defKOEA{1.9,2.2}
            defFOEA{1.4,1}

            defKOEB{3.3,2.2}
            defFOEB{1.2,1}

            defKOEC{2.75,1.4}
            defFOEC{1.4,1}

            defKOEO{2.5,2}
            defFOEO{2.5,2.0}

            NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
            psellipse(KOEA)(FOEA)}%
            }

            NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
            psellipse(KOEB)(FOEB)}%
            }

            NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
            psellipse(KOEC)(FOEC)}%
            }

            NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
            psellipse(KOEO)(FOEO)}%
            }

            NewDocumentCommand{EndeEllipsen}{sm}{%
            EreignisOmega%
            pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
            pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
            EreignisA
            EreignisB
            EreignisC
            rput[t](E){#2}%
            IfBooleanF{#1}{%
            rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
            rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
            rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
            rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
            }%
            }

            NewDocumentCommand{codeclip}{m}{%
            pscustom[linestyle=none]{%
            code{/clip /eoclip load def}%
            psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
            #1
            }%
            }

            %ExplSyntaxOn
            % We could use some automated macro creation but well
            % 000
            NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisOmega*[#1][#2]%
            endpsclip
            }%
            % 001
            NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }
            % 010
            NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisB*[#1][#2]%
            endpsclip
            }
            % 011
            NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisA
            }%
            }%
            EreignisB*[#1][#2]%
            EreignisC*[#1][#2]%
            endpsclip
            }
            % 100
            NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }
            % 101
            NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisC
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisA*[#1][#2]%
            EreignisC*[#1][#2]%
            endpsclip
            }
            % 110
            NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            EreignisB*[#1][#2]%
            endpsclip
            }
            % 111
            NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            }%
            codeclip{%
            EreignisA
            EreignisC
            }%
            codeclip{%
            EreignisB
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            EreignisB*[#1][#2]%
            EreignisC*[#1][#2]%
            endpsclip
            }
            %ExplSyntaxOff

            %xintverbosetrue
            makeatletter
            newcommandVennFromTeX[1]{%
            VennFromTeX@main #1%
            }%
            defVennFromTeX@main$#1${%
            begingroup
            xintglobaldefstrue
            defoverline##1{!(##1)}% or not(##1)
            defcap{&&}% or 'and'
            defcup{||}% or 'or'
            defoplus{ 'xor' }%
            defsetminus##1{ifx(##1&&!(else &&!(##1)fi}%
            letbiglempty
            letbigrempty
            % ....
            % (add above all needed extra definitions: letBiglempty etc...)
            xintdeffunc MyBool(A, B, C) := #1;% #1 must use A, B, C only
            endgroup
            % we could make a loop here (using @Roman), but let's stay simple
            % I trust xparse experts can wrap this up in macros allowing to customize
            % the colors
            % ATTENTION THAT THESE arealI...VIII ARE NOT THE SAME AS IN @THOMAS ANSWER
            xintifboolexpr{MyBool(0, 0, 0)}{arealI[cyan][0.8]}{}%
            xintifboolexpr{MyBool(0, 0, 1)}{arealII[cyan][0.8]}{}%
            xintifboolexpr{MyBool(0, 1, 0)}{arealIII[cyan][0.8]}{}%
            xintifboolexpr{MyBool(0, 1, 1)}{arealIV[cyan][0.8]}{}%
            xintifboolexpr{MyBool(1, 0, 0)}{arealV[cyan][0.8]}{}%
            xintifboolexpr{MyBool(1, 0, 1)}{arealVI[cyan][0.8]}{}%
            xintifboolexpr{MyBool(1, 1, 0)}{arealVII[cyan][0.8]}{}%
            xintifboolexpr{MyBool(1, 1, 1)}{arealVIII[cyan][0.8]}{}%
            EndeEllipsen{$#1$}%
            }%
            makeatother

            begin{document}

            %testing if I, II, ..., VIII are as expected
            % makeatletter
            % xintFor*#1in{xintSeq{0}{7}}do{%
            % begin{pspicture}(0,-1)(5,4)
            % rput(2,0){thenumexpr1+#1}
            % @nameuse{areal@Roman{numexpr1+#1}}[cyan][0.8]
            % EndeEllipsen{}
            % end{pspicture}
            % }%
            % end{document}


            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$Acap Bcap C$}%
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$Acap (Bcup C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$(overline{A}cap overline{B})cup C$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$overline{A}setminus (Bcap C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$(overline{A}setminus B)cap C$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$(Asetminus B)cup (Bcap C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennFromTeX{$Aoplus Boplus C$}
            end{pspicture}

            end{document}


            Produces



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here







            Here is code to generate all 256 Venn diagrams. Just insert it in body of above document and don't forget to add usepackage{xintbinhex} to preamble.



            % generating all graphics

            % 0<= n <= 255 has eight binary digits
            % abcdefgh
            % a=1 -> region VIII is included (A cap B cap C)
            % b=1 -> region VII is included
            % ...
            % h=1 -> region I is included (overline{A}cap overline{B} cap overline{C})
            % We want also to describe the region as a formula...
            % We could use 8 xintFor loops #1, ..., #8, but then
            % we still need to convert #1*7 to binary, #2*6, #3*5 etc...
            % I thus use xintbinhex per convenience but ifodd would be enough
            % As I use xintbinhex, I also use a single xintFor* loop

            %defgobbleone#1{}%
            defgobbletwo#1#2{}%
            xintFor* #1 in {xintSeq{0}{255}}:
            {%
            xintDigitsOfxintDecToBin{thenumexpr256+#1relax}toRegions
            % due to leading 1 there will be a shift of indexing in Regions
            edefx{xintifboolexpr{Regions{thenumexpr9-0}}% 000
            {unexpanded{allowbreakcup
            overline{A}capoverline{B}capoverline{C}}}%
            {}%
            xintifboolexpr{Regions{9-1}}% 001
            {unexpanded{allowbreakcup overline{A}capoverline{B}cap C}}%
            {}%
            xintifboolexpr{Regions{9-2}}% 010
            {unexpanded{allowbreakcup overline{A}cap B capoverline{C}}}%
            {}%
            xintifboolexpr{Regions{9-3}}% 011
            {unexpanded{allowbreakcup overline{A} cap B cap C}}%
            {}%
            xintifboolexpr{Regions{9-4}}% 100
            {unexpanded{allowbreakcup Acap overline{B}cap overline{C}}}%
            {}%
            xintifboolexpr{Regions{9-5}}% 101
            {unexpanded{allowbreakcup Acap overline{B}cap C}}%
            {}%
            xintifboolexpr{Regions{9-6}}% 110
            {unexpanded{allowbreakcup Acap Bcap overline{C}}}%
            {}%
            xintifboolexpr{Regions{9-7}}% 111
            {unexpanded{allowbreakcup Acap B cap C}}%
            {}%
            }%
            xintifForFirst{defx{emptyset}}
            {oodefx{expandaftergobbletwox}}%
            begin{pspicture}(0,-2)(5,4)
            % I will leave here each Region as individual call, so a color can
            % be added by modifying this code
            xintifboolexpr{Regions{9-0}}{arealI[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-1}}{arealII[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-2}}{arealIII[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-3}}{arealIV[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-4}}{arealV[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-5}}{arealVI[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-6}}{arealVII[cyan][0.8]}{}%
            xintifboolexpr{Regions{9-7}}{arealVIII[cyan][0.8]}{}%
            EndeEllipsen{parbox{4cm}{centering$x$}}%
            end{pspicture}%
            }%


            Defect: the description of the set is as a disjoint union of atomic events. There might be some canonical shorter description but I never really thought about it. For example one of those diagram will represent $Omegasetminus A$ but this not the way it will be legended.



            Here is how this example comes out (on page 16 of document with nothing else, i.e. it corresponds to #1 = 15 in the loop, 15=1111 means to keep atomic events 0=000, 1=001, 2=010, 3=011, which is complement of A in Omega.



            enter image description here







            Here is now with 4 sets.



            This time, with TikZ code (I know neither PSTricks nor TikZ and can only survive from copying pre-existing drawing instructions; in this case I started from https://tex.stackexchange.com/a/100091/4686 by @JohnHammersley in 2013).



            First I include an image of all atomic events, which are the regions to which the Atomic... macros in code next refer. (this was done for checking while preparing answer)



            enter image description here



            Here is the code for VennFromTeX, use it as VennFromTeX{$ set formula with A, B, C, D $}. Same instructions as above for three sets.
            (one may wish to enlarge the syntax for example by allowing use of U or Omega and defining it in xintexpr to be simply 1, and similarly emptyset could be defined to be 0).



            documentclass[12pt, tikz, border=10pt]{standalone}

            usepackage{tikz}

            usetikzlibrary{positioning,shapes.geometric}

            usepackage{xintexpr}% for VennFromTeX


            % For drawing
            deffirstellip{(-1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
            defsecondellip{(-0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=-50]}
            defthirdellip{(0.3, 1cm) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}
            deffourthellip{(1.6, 0) ellipse [x radius=3cm, y radius=1.5cm, rotate=50]}

            defbounding{(-5,-3) rectangle (5,4)}

            % Elementary sets
            % ABCD
            % abcd a, b, c, d in {0, 1}
            defAtomic{% 0000
            begin{scope}[even odd rule]% exterior
            clip firstellip (-5,-5) rectangle (5,5);
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] bounding;
            end{scope}
            }%
            defAtomici{% 0001
            begin{scope}[even odd rule]% fourth ellipse corner
            clip firstellip (-5,-5) rectangle (5,5);
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            fill[yellow] fourthellip;
            end{scope}
            }%
            defAtomicii{% 0010
            begin{scope}[even odd rule]% third ellipse corner
            clip firstellip (-5,-5) rectangle (5,5);
            clip secondellip (-5,-5) rectangle (5,5);
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] thirdellip;
            end{scope}
            }%
            defAtomiciii{% 0011
            begin{scope}[even odd rule]%
            clip firstellip (-5,-5) rectangle (5,5);
            clip secondellip (-5,-5) rectangle (5,5);
            clip fourthellip;
            fill[yellow] thirdellip;
            end{scope}
            }%
            defAtomiciv{% 0100
            begin{scope}[even odd rule]% second ellipse corner
            clip firstellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] secondellip;
            end{scope}
            }%
            defAtomicv{% 0101
            begin{scope}[even odd rule]%
            clip firstellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip;
            fill[yellow] secondellip;
            end{scope}
            }%
            defAtomicvi{% 0110
            begin{scope}[even odd rule]%
            clip firstellip (-5,-5) rectangle (5,5);
            clip thirdellip;
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] secondellip;
            end{scope}
            }%
            defAtomicvii{% 0111
            begin{scope}[even odd rule]%
            clip firstellip (-5,-5) rectangle (5,5);
            clip thirdellip;
            clip fourthellip;
            fill[yellow] secondellip;
            end{scope}
            }%
            defAtomicviii{% 1000
            begin{scope}[even odd rule]%
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicix{% 1001
            begin{scope}[even odd rule]%
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip;
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicx{% 1010
            begin{scope}[even odd rule]%
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip;
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicxi{% 1011
            begin{scope}[even odd rule]%
            clip secondellip (-5,-5) rectangle (5,5);
            clip thirdellip;
            clip fourthellip;
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicxii{% 1100
            begin{scope}[even odd rule]%
            clip secondellip;
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicxiii{% 1101
            begin{scope}[even odd rule]%
            clip secondellip;
            clip thirdellip (-5,-5) rectangle (5,5);
            clip fourthellip;
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicxiv{% 1110
            begin{scope}[even odd rule]%
            clip secondellip;
            clip thirdellip;
            clip fourthellip (-5,-5) rectangle (5,5);
            fill[yellow] firstellip;
            end{scope}
            }%
            defAtomicxv{% 1111
            begin{scope}[even odd rule]%
            clip secondellip;
            clip thirdellip;
            clip fourthellip;
            fill[yellow] firstellip;
            end{scope}
            }%

            makeatletter
            newcommandVennFromTeX[1]{VennFromTeX@main #1}%

            defVennFromTeX@main$#1${%
            begingroup
            xintglobaldefstrue
            defoverline##1{!(##1)}% or not(##1)
            defcap{&&}% or 'and'
            defcup{||}% or 'or'
            defoplus{ 'xor' }%
            defsetminus##1{ifx(##1&&!(else &&!(##1)fi}%
            letbiglempty
            letbigrempty
            % ....
            % (add above all needed extra definitions: letBiglempty etc...)
            xintdeffunc MyBool(A, B, C, D) := #1;% #1 must use A, B, C, Donly
            endgroup
            begin{tikzpicture}

            xintFor* ##1 in {01}:
            {%
            xintFor* ##2 in {01}:
            {%
            xintFor* ##3 in {01}:
            {%
            xintFor* ##4 in {01}:
            {%
            xintifboolexpr{MyBool(##1, ##2, ##3, ##4)}
            {csname
            Atomicromannumeralnumexpr##1*8+##2*4+##3*2+##4endcsname}%
            {}%
            }%
            }%
            }%
            }%
            draw bounding;

            % fill[white] firstellip;
            % fill[white] secondellip;
            % fill[white] thirdellip;
            % fill[white] fourthellip;

            draw firstellip node [label={[xshift=-2cm, yshift=-0.9cm]$A$}] {};
            draw secondellip node [label={[xshift=-2.1cm, yshift=2.1cm]$B$}] {};
            draw thirdellip node [label={[xshift=2.1cm, yshift=2.1cm]$C$}] {};
            draw fourthellip node [label={[xshift=2cm, yshift=-0.9cm]$D$}] {};

            draw bounding node [label=below left:$U$] {};

            draw (0, 0) node [yshift=+4.4cm] {$#1$};

            end{tikzpicture}
            }%
            makeatother
            begin{document}

            % xintverbosetrue

            VennFromTeX{$Acap Bcap Ccap D$}

            VennFromTeX{$(Acap B)cup (Ccap D)$}

            VennFromTeX{$(overline{A}cupoverline{B})cap(overline{C}cupoverline{D})$}

            % attention to use parentheses for disambiguating setminus

            VennFromTeX{$(Acup B cup C) setminus(Bcup Ccup D)$}

            VennFromTeX{$(Acup B cup C) cap (Bcup Ccup D)$}

            VennFromTeX{$((Asetminus (Bcup Ccup D)) cup Bcap Ccap
            D)setminus (Acap Bcap Ccap D)$}

            end{document}


            Be careful to read the caveat top regarding usage of setminus in input.



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            enter image description here



            and finally



            enter image description here







            share|improve this answer














            share|improve this answer



            share|improve this answer








            edited Dec 2 at 22:39

























            answered Dec 2 at 11:00









            jfbu

            46k66148




            46k66148












            • (+1) Thank you for your answer!
              – chishimotoji
              Dec 2 at 11:27










            • (+1) Wow, fantastic!
              – Thomas
              Dec 2 at 11:34






            • 1




              Encyclopedic answer
              – Diaa
              Dec 2 at 11:38










            • careful in first part of answer when inputting a long formula that it some parts may be cut off the page, check the parbox in second part how to work around that, and I also increased the vertical dimension.
              – jfbu
              Dec 2 at 12:46






            • 2




              @ArtificialStupidity I have to get dinner but just give me time to learn PSTricks and I can do with 4 sets afterwards...
              – jfbu
              Dec 2 at 18:39


















            • (+1) Thank you for your answer!
              – chishimotoji
              Dec 2 at 11:27










            • (+1) Wow, fantastic!
              – Thomas
              Dec 2 at 11:34






            • 1




              Encyclopedic answer
              – Diaa
              Dec 2 at 11:38










            • careful in first part of answer when inputting a long formula that it some parts may be cut off the page, check the parbox in second part how to work around that, and I also increased the vertical dimension.
              – jfbu
              Dec 2 at 12:46






            • 2




              @ArtificialStupidity I have to get dinner but just give me time to learn PSTricks and I can do with 4 sets afterwards...
              – jfbu
              Dec 2 at 18:39
















            (+1) Thank you for your answer!
            – chishimotoji
            Dec 2 at 11:27




            (+1) Thank you for your answer!
            – chishimotoji
            Dec 2 at 11:27












            (+1) Wow, fantastic!
            – Thomas
            Dec 2 at 11:34




            (+1) Wow, fantastic!
            – Thomas
            Dec 2 at 11:34




            1




            1




            Encyclopedic answer
            – Diaa
            Dec 2 at 11:38




            Encyclopedic answer
            – Diaa
            Dec 2 at 11:38












            careful in first part of answer when inputting a long formula that it some parts may be cut off the page, check the parbox in second part how to work around that, and I also increased the vertical dimension.
            – jfbu
            Dec 2 at 12:46




            careful in first part of answer when inputting a long formula that it some parts may be cut off the page, check the parbox in second part how to work around that, and I also increased the vertical dimension.
            – jfbu
            Dec 2 at 12:46




            2




            2




            @ArtificialStupidity I have to get dinner but just give me time to learn PSTricks and I can do with 4 sets afterwards...
            – jfbu
            Dec 2 at 18:39




            @ArtificialStupidity I have to get dinner but just give me time to learn PSTricks and I can do with 4 sets afterwards...
            – jfbu
            Dec 2 at 18:39











            12














            documentclass[pstricks]{standalone}
            begin{document}
            begin{pspicture}(-5,-5)(5,5)
            pscustom[fillstyle=eofill,fillcolor=blue,linecolor=blue]{%
            pscircle(1.5;90){3}
            pscircle(1.5;-30){3}
            pscircle(1.5;210){3}
            }
            end{pspicture}
            end{document}


            enter image description here



            Some other simple example:



            documentclass[pstricks]{standalone}
            usepackage{pstricks}
            begin{document}
            begin{pspicture}(-3.2,-3.2)(3.2,3.2)
            pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
            psclip{pscircle(-1,0.5){1.5}% these object(s) will clip
            pscircle(1,0.5){1.5}}
            pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}% from this object
            endpsclip
            pscircle(-1,0.5){1.5}% to get the clipped circle lines
            pscircle(0,-1){1.5}
            pscircle(1,0.5){1.5}
            end{pspicture}

            begin{pspicture}(-3.2,-3.2)(3.2,3.2)
            pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
            psclip{pscircle(-1,0.5){1.5}}
            pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}
            pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
            endpsclip
            pscircle(-1,0.5){1.5}
            pscircle(0,-1){1.5}
            pscircle(1,0.5){1.5}
            end{pspicture}

            begin{pspicture}(-3.2,-3.2)(3.2,3.2)
            pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
            psclip{pscircle(0,-1){1.5}}
            pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
            pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
            endpsclip
            pscircle(-1,0.5){1.5}
            pscircle(0,-1){1.5}
            pscircle(1,0.5){1.5}
            end{pspicture}

            begin{pspicture}(-3.2,-3.2)(3.2,3.2)
            pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
            psclip{pscircle(0,-1){1.5}}
            pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
            endpsclip
            pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
            pscircle(0,-1){1.5}
            pscircle(1,0.5){1.5}
            end{pspicture}

            end{document}


            enter image description hereenter image description here






            share|improve this answer



















            • 1




              I haven't known that there is a option as " fillstyle=eofill " before. It doesn't within PStrick User's Guide.
              – chishimotoji
              Nov 30 at 8:38






            • 1




              tug.org/PSTricks/main.cgi?file=Examples/Box/boxfill#2
              – Herbert
              Nov 30 at 11:20










            • I am really impressived by your code. Only with psclip,pscustom, you created some the interesting result. I have deleted more three comments before. May be my knowledge about psclip is not enough to generate several thing which I want. :((((
              – chishimotoji
              Dec 2 at 15:38








            • 2




              clipping is nothing else than taking a knife let it go along a circle or two corcles and cut everything from a given cake. psclip{the way of the knife} ... the cake .. endpsclip
              – Herbert
              Dec 2 at 15:41
















            12














            documentclass[pstricks]{standalone}
            begin{document}
            begin{pspicture}(-5,-5)(5,5)
            pscustom[fillstyle=eofill,fillcolor=blue,linecolor=blue]{%
            pscircle(1.5;90){3}
            pscircle(1.5;-30){3}
            pscircle(1.5;210){3}
            }
            end{pspicture}
            end{document}


            enter image description here



            Some other simple example:



            documentclass[pstricks]{standalone}
            usepackage{pstricks}
            begin{document}
            begin{pspicture}(-3.2,-3.2)(3.2,3.2)
            pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
            psclip{pscircle(-1,0.5){1.5}% these object(s) will clip
            pscircle(1,0.5){1.5}}
            pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}% from this object
            endpsclip
            pscircle(-1,0.5){1.5}% to get the clipped circle lines
            pscircle(0,-1){1.5}
            pscircle(1,0.5){1.5}
            end{pspicture}

            begin{pspicture}(-3.2,-3.2)(3.2,3.2)
            pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
            psclip{pscircle(-1,0.5){1.5}}
            pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}
            pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
            endpsclip
            pscircle(-1,0.5){1.5}
            pscircle(0,-1){1.5}
            pscircle(1,0.5){1.5}
            end{pspicture}

            begin{pspicture}(-3.2,-3.2)(3.2,3.2)
            pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
            psclip{pscircle(0,-1){1.5}}
            pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
            pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
            endpsclip
            pscircle(-1,0.5){1.5}
            pscircle(0,-1){1.5}
            pscircle(1,0.5){1.5}
            end{pspicture}

            begin{pspicture}(-3.2,-3.2)(3.2,3.2)
            pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
            psclip{pscircle(0,-1){1.5}}
            pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
            endpsclip
            pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
            pscircle(0,-1){1.5}
            pscircle(1,0.5){1.5}
            end{pspicture}

            end{document}


            enter image description hereenter image description here






            share|improve this answer



















            • 1




              I haven't known that there is a option as " fillstyle=eofill " before. It doesn't within PStrick User's Guide.
              – chishimotoji
              Nov 30 at 8:38






            • 1




              tug.org/PSTricks/main.cgi?file=Examples/Box/boxfill#2
              – Herbert
              Nov 30 at 11:20










            • I am really impressived by your code. Only with psclip,pscustom, you created some the interesting result. I have deleted more three comments before. May be my knowledge about psclip is not enough to generate several thing which I want. :((((
              – chishimotoji
              Dec 2 at 15:38








            • 2




              clipping is nothing else than taking a knife let it go along a circle or two corcles and cut everything from a given cake. psclip{the way of the knife} ... the cake .. endpsclip
              – Herbert
              Dec 2 at 15:41














            12












            12








            12






            documentclass[pstricks]{standalone}
            begin{document}
            begin{pspicture}(-5,-5)(5,5)
            pscustom[fillstyle=eofill,fillcolor=blue,linecolor=blue]{%
            pscircle(1.5;90){3}
            pscircle(1.5;-30){3}
            pscircle(1.5;210){3}
            }
            end{pspicture}
            end{document}


            enter image description here



            Some other simple example:



            documentclass[pstricks]{standalone}
            usepackage{pstricks}
            begin{document}
            begin{pspicture}(-3.2,-3.2)(3.2,3.2)
            pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
            psclip{pscircle(-1,0.5){1.5}% these object(s) will clip
            pscircle(1,0.5){1.5}}
            pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}% from this object
            endpsclip
            pscircle(-1,0.5){1.5}% to get the clipped circle lines
            pscircle(0,-1){1.5}
            pscircle(1,0.5){1.5}
            end{pspicture}

            begin{pspicture}(-3.2,-3.2)(3.2,3.2)
            pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
            psclip{pscircle(-1,0.5){1.5}}
            pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}
            pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
            endpsclip
            pscircle(-1,0.5){1.5}
            pscircle(0,-1){1.5}
            pscircle(1,0.5){1.5}
            end{pspicture}

            begin{pspicture}(-3.2,-3.2)(3.2,3.2)
            pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
            psclip{pscircle(0,-1){1.5}}
            pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
            pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
            endpsclip
            pscircle(-1,0.5){1.5}
            pscircle(0,-1){1.5}
            pscircle(1,0.5){1.5}
            end{pspicture}

            begin{pspicture}(-3.2,-3.2)(3.2,3.2)
            pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
            psclip{pscircle(0,-1){1.5}}
            pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
            endpsclip
            pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
            pscircle(0,-1){1.5}
            pscircle(1,0.5){1.5}
            end{pspicture}

            end{document}


            enter image description hereenter image description here






            share|improve this answer














            documentclass[pstricks]{standalone}
            begin{document}
            begin{pspicture}(-5,-5)(5,5)
            pscustom[fillstyle=eofill,fillcolor=blue,linecolor=blue]{%
            pscircle(1.5;90){3}
            pscircle(1.5;-30){3}
            pscircle(1.5;210){3}
            }
            end{pspicture}
            end{document}


            enter image description here



            Some other simple example:



            documentclass[pstricks]{standalone}
            usepackage{pstricks}
            begin{document}
            begin{pspicture}(-3.2,-3.2)(3.2,3.2)
            pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
            psclip{pscircle(-1,0.5){1.5}% these object(s) will clip
            pscircle(1,0.5){1.5}}
            pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}% from this object
            endpsclip
            pscircle(-1,0.5){1.5}% to get the clipped circle lines
            pscircle(0,-1){1.5}
            pscircle(1,0.5){1.5}
            end{pspicture}

            begin{pspicture}(-3.2,-3.2)(3.2,3.2)
            pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
            psclip{pscircle(-1,0.5){1.5}}
            pscircle[fillstyle=solid,fillcolor=red!40](0,-1){1.5}
            pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
            endpsclip
            pscircle(-1,0.5){1.5}
            pscircle(0,-1){1.5}
            pscircle(1,0.5){1.5}
            end{pspicture}

            begin{pspicture}(-3.2,-3.2)(3.2,3.2)
            pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
            psclip{pscircle(0,-1){1.5}}
            pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
            pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
            endpsclip
            pscircle(-1,0.5){1.5}
            pscircle(0,-1){1.5}
            pscircle(1,0.5){1.5}
            end{pspicture}

            begin{pspicture}(-3.2,-3.2)(3.2,3.2)
            pscircle[fillstyle=solid,fillcolor=blue!40](0,0){3}
            psclip{pscircle(0,-1){1.5}}
            pscircle[fillstyle=solid,fillcolor=red!40](1,0.5){1.5}
            endpsclip
            pscircle[fillstyle=solid,fillcolor=red!40](-1,0.5){1.5}
            pscircle(0,-1){1.5}
            pscircle(1,0.5){1.5}
            end{pspicture}

            end{document}


            enter image description hereenter image description here







            share|improve this answer














            share|improve this answer



            share|improve this answer








            edited Dec 2 at 15:19

























            answered Nov 30 at 8:09









            Herbert

            269k24408717




            269k24408717








            • 1




              I haven't known that there is a option as " fillstyle=eofill " before. It doesn't within PStrick User's Guide.
              – chishimotoji
              Nov 30 at 8:38






            • 1




              tug.org/PSTricks/main.cgi?file=Examples/Box/boxfill#2
              – Herbert
              Nov 30 at 11:20










            • I am really impressived by your code. Only with psclip,pscustom, you created some the interesting result. I have deleted more three comments before. May be my knowledge about psclip is not enough to generate several thing which I want. :((((
              – chishimotoji
              Dec 2 at 15:38








            • 2




              clipping is nothing else than taking a knife let it go along a circle or two corcles and cut everything from a given cake. psclip{the way of the knife} ... the cake .. endpsclip
              – Herbert
              Dec 2 at 15:41














            • 1




              I haven't known that there is a option as " fillstyle=eofill " before. It doesn't within PStrick User's Guide.
              – chishimotoji
              Nov 30 at 8:38






            • 1




              tug.org/PSTricks/main.cgi?file=Examples/Box/boxfill#2
              – Herbert
              Nov 30 at 11:20










            • I am really impressived by your code. Only with psclip,pscustom, you created some the interesting result. I have deleted more three comments before. May be my knowledge about psclip is not enough to generate several thing which I want. :((((
              – chishimotoji
              Dec 2 at 15:38








            • 2




              clipping is nothing else than taking a knife let it go along a circle or two corcles and cut everything from a given cake. psclip{the way of the knife} ... the cake .. endpsclip
              – Herbert
              Dec 2 at 15:41








            1




            1




            I haven't known that there is a option as " fillstyle=eofill " before. It doesn't within PStrick User's Guide.
            – chishimotoji
            Nov 30 at 8:38




            I haven't known that there is a option as " fillstyle=eofill " before. It doesn't within PStrick User's Guide.
            – chishimotoji
            Nov 30 at 8:38




            1




            1




            tug.org/PSTricks/main.cgi?file=Examples/Box/boxfill#2
            – Herbert
            Nov 30 at 11:20




            tug.org/PSTricks/main.cgi?file=Examples/Box/boxfill#2
            – Herbert
            Nov 30 at 11:20












            I am really impressived by your code. Only with psclip,pscustom, you created some the interesting result. I have deleted more three comments before. May be my knowledge about psclip is not enough to generate several thing which I want. :((((
            – chishimotoji
            Dec 2 at 15:38






            I am really impressived by your code. Only with psclip,pscustom, you created some the interesting result. I have deleted more three comments before. May be my knowledge about psclip is not enough to generate several thing which I want. :((((
            – chishimotoji
            Dec 2 at 15:38






            2




            2




            clipping is nothing else than taking a knife let it go along a circle or two corcles and cut everything from a given cake. psclip{the way of the knife} ... the cake .. endpsclip
            – Herbert
            Dec 2 at 15:41




            clipping is nothing else than taking a knife let it go along a circle or two corcles and cut everything from a given cake. psclip{the way of the knife} ... the cake .. endpsclip
            – Herbert
            Dec 2 at 15:41











            9














            A TikZ solution for comparison purposes.



            documentclass{article}
            usepackage{tikz}
            begin{document}
            begin{tikzpicture}
            draw[even odd rule,fill=blue](0,0)circle(3)(4,0)circle(3)(2,3)circle(3);
            end{tikzpicture}
            end{document}


            Venn



            Update: To answer @ArtificialStupidity's comment



            Here is a solution with different coordinate points from those of the question asked by the OP. The centres of the circles form an equilateral triangle here.



            documentclass{article}
            usepackage{tikz}
            begin{document}
            begin{tikzpicture}
            draw[even odd rule,fill=blue](0,0)circle(3)(3,0)circle(3)(60:3)circle(3);
            end{tikzpicture}
            end{document}


            venn-2






            share|improve this answer























            • @ArtificialStupidity Yes, as in the figure given as an example by the OP. I didn't change the coordinates.
              – AndréC
              Nov 30 at 12:05










            • +1 for the equilateral triangle Δ
              – stendarr
              Nov 30 at 14:03
















            9














            A TikZ solution for comparison purposes.



            documentclass{article}
            usepackage{tikz}
            begin{document}
            begin{tikzpicture}
            draw[even odd rule,fill=blue](0,0)circle(3)(4,0)circle(3)(2,3)circle(3);
            end{tikzpicture}
            end{document}


            Venn



            Update: To answer @ArtificialStupidity's comment



            Here is a solution with different coordinate points from those of the question asked by the OP. The centres of the circles form an equilateral triangle here.



            documentclass{article}
            usepackage{tikz}
            begin{document}
            begin{tikzpicture}
            draw[even odd rule,fill=blue](0,0)circle(3)(3,0)circle(3)(60:3)circle(3);
            end{tikzpicture}
            end{document}


            venn-2






            share|improve this answer























            • @ArtificialStupidity Yes, as in the figure given as an example by the OP. I didn't change the coordinates.
              – AndréC
              Nov 30 at 12:05










            • +1 for the equilateral triangle Δ
              – stendarr
              Nov 30 at 14:03














            9












            9








            9






            A TikZ solution for comparison purposes.



            documentclass{article}
            usepackage{tikz}
            begin{document}
            begin{tikzpicture}
            draw[even odd rule,fill=blue](0,0)circle(3)(4,0)circle(3)(2,3)circle(3);
            end{tikzpicture}
            end{document}


            Venn



            Update: To answer @ArtificialStupidity's comment



            Here is a solution with different coordinate points from those of the question asked by the OP. The centres of the circles form an equilateral triangle here.



            documentclass{article}
            usepackage{tikz}
            begin{document}
            begin{tikzpicture}
            draw[even odd rule,fill=blue](0,0)circle(3)(3,0)circle(3)(60:3)circle(3);
            end{tikzpicture}
            end{document}


            venn-2






            share|improve this answer














            A TikZ solution for comparison purposes.



            documentclass{article}
            usepackage{tikz}
            begin{document}
            begin{tikzpicture}
            draw[even odd rule,fill=blue](0,0)circle(3)(4,0)circle(3)(2,3)circle(3);
            end{tikzpicture}
            end{document}


            Venn



            Update: To answer @ArtificialStupidity's comment



            Here is a solution with different coordinate points from those of the question asked by the OP. The centres of the circles form an equilateral triangle here.



            documentclass{article}
            usepackage{tikz}
            begin{document}
            begin{tikzpicture}
            draw[even odd rule,fill=blue](0,0)circle(3)(3,0)circle(3)(60:3)circle(3);
            end{tikzpicture}
            end{document}


            venn-2







            share|improve this answer














            share|improve this answer



            share|improve this answer








            edited Nov 30 at 12:11

























            answered Nov 30 at 11:05









            AndréC

            7,63011440




            7,63011440












            • @ArtificialStupidity Yes, as in the figure given as an example by the OP. I didn't change the coordinates.
              – AndréC
              Nov 30 at 12:05










            • +1 for the equilateral triangle Δ
              – stendarr
              Nov 30 at 14:03


















            • @ArtificialStupidity Yes, as in the figure given as an example by the OP. I didn't change the coordinates.
              – AndréC
              Nov 30 at 12:05










            • +1 for the equilateral triangle Δ
              – stendarr
              Nov 30 at 14:03
















            @ArtificialStupidity Yes, as in the figure given as an example by the OP. I didn't change the coordinates.
            – AndréC
            Nov 30 at 12:05




            @ArtificialStupidity Yes, as in the figure given as an example by the OP. I didn't change the coordinates.
            – AndréC
            Nov 30 at 12:05












            +1 for the equilateral triangle Δ
            – stendarr
            Nov 30 at 14:03




            +1 for the equilateral triangle Δ
            – stendarr
            Nov 30 at 14:03











            8














            With this definitions every surface can be colored.



            documentclass[pstricks]{standalone}
            usepackage{pst-node}
            usepackage{xparse,xintexpr}

            defradiusK{xinttheiexpr[6] 2*sqrt(3)/3relax}

            defKOEA{2.5,2}
            defFOEA{radiusK,radiusK}

            defKOEB{2,1}
            defFOEB{radiusK,radiusK}

            defKOEC{3,1}
            defFOEC{radiusK,radiusK}

            defKOEO{2.5,1.375}
            defFOEO{2.5,2.5}

            %uncomment the following lines to have ellipses
            %defKOEA{1.9,2.2}
            %defFOEA{1.4,1}
            %
            %defKOEB{3.3,2.2}
            %defFOEB{1.2,1}
            %
            %defKOEC{2.75,1.4}
            %defFOEC{1.4,1}
            %
            %defKOEO{2.5,2}
            %defFOEO{2.5,2.0}

            NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
            psellipse(KOEA)(FOEA)}%
            }

            NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
            psellipse(KOEB)(FOEB)}%
            }

            NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
            psellipse(KOEC)(FOEC)}%
            }

            NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
            psellipse(KOEO)(FOEO)}%
            }

            NewDocumentCommand{EndeEllipsen}{sm}{%
            EreignisOmega%
            pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
            pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
            EreignisA
            EreignisB
            EreignisC
            rput[t](E){#2}%
            IfBooleanF{#1}{%
            rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
            rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
            rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
            rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
            }%
            }

            NewDocumentCommand{codeclip}{m}{%
            pscustom[linestyle=none]{%
            code{/clip /eoclip load def}%
            psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
            #1
            }%
            }

            NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisOmega*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisB*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
            psclip{EreignisB}
            psclip{EreignisC}%
            EreignisA*[#1][#2]%
            endpsclip
            endpsclip
            }

            NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisA
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }

            begin{document}


            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            EndeEllipsen*{$Asetminus C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealVI
            EndeEllipsen*{$Acap Bcap C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealIII
            arealV
            arealVI
            EndeEllipsen*{$Acap (Bcup C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            EreignisC*%
            EndeEllipsen*{$(overline{A}cap overline{B})cup C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            arealIV
            arealVIII
            EndeEllipsen*{$overline{A}setminus (Bcap C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealVIII
            EndeEllipsen*{$(overline{A}setminus B)cap C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealII
            arealV
            arealVI
            arealVII
            EndeEllipsen*{$(Asetminus B)cup (Bcap C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealIII
            arealV
            EndeEllipsen*{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
            end{pspicture}


            end{document}




            Perhaps you want to check out this.



            documentclass[pstricks]{standalone}
            usepackage{pst-node}
            usepackage{xparse,xintexpr}

            %defradiusK{xinttheiexpr[6] 2*sqrt(3)/3relax}
            %
            %defKOEA{2.5,2}
            %defFOEA{radiusK,radiusK}
            %
            %defKOEB{2,1}
            %defFOEB{radiusK,radiusK}
            %
            %defKOEC{3,1}
            %defFOEC{radiusK,radiusK}
            %
            %defKOEO{2.5,1.375}
            %defFOEO{2.5,2.5}

            %uncomment the following lines to have ellipses
            defKOEA{1.9,2.2}
            defFOEA{1.4,1}

            defKOEB{3.3,2.2}
            defFOEB{1.2,1}

            defKOEC{2.75,1.4}
            defFOEC{1.4,1}

            defKOEO{2.5,2}
            defFOEO{2.5,2.0}

            NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
            psellipse(KOEA)(FOEA)}%
            }

            NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
            psellipse(KOEB)(FOEB)}%
            }

            NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
            psellipse(KOEC)(FOEC)}%
            }

            NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
            psellipse(KOEO)(FOEO)}%
            }

            NewDocumentCommand{EndeEllipsen}{sm}{%
            EreignisOmega%
            pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
            pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
            EreignisA
            EreignisB
            EreignisC
            rput[t](E){#2}%
            IfBooleanF{#1}{%
            rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
            rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
            rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
            rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
            }%
            }

            NewDocumentCommand{codeclip}{m}{%
            pscustom[linestyle=none]{%
            code{/clip /eoclip load def}%
            psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
            #1
            }%
            }

            NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisOmega*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisB*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
            psclip{EreignisB}
            psclip{EreignisC}%
            EreignisA*[#1][#2]%
            endpsclip
            endpsclip
            }

            NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisA
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }

            begin{document}


            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            EndeEllipsen{$Asetminus C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealVI
            EndeEllipsen{$Acap Bcap C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealIII
            arealV
            arealVI
            EndeEllipsen{$Acap (Bcup C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            EreignisC*%
            EndeEllipsen{$(overline{A}cap overline{B})cup C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            arealIV
            arealVIII
            EndeEllipsen{$overline{A}setminus (Bcap C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealVIII
            EndeEllipsen{$(overline{A}setminus B)cap C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealII
            arealV
            arealVI
            arealVII
            EndeEllipsen{$(Asetminus B)cup (Bcap C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealIII
            arealV
            EndeEllipsen{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
            end{pspicture}


            end{document}




            With the help of xint-package using xintFor and xintForpair you can write



            VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%


            so every surface becomes an own color, or you write



            VennIII[blue](0.5){2,4,6,8}{Text}%


            and all becomes color blue with opacity 0.5.



            documentclass[pstricks]{standalone}
            usepackage{pst-node}
            usepackage{xparse,xintexpr}

            defKOEA{1.9,2.2}
            defFOEA{1.4,1}

            defKOEB{3.3,2.2}
            defFOEB{1.2,1}

            defKOEC{2.75,1.4}
            defFOEC{1.4,1}

            defKOEO{2.5,2}
            defFOEO{2.5,2.0}

            NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
            psellipse(KOEA)(FOEA)}%
            }

            NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
            psellipse(KOEB)(FOEB)}%
            }

            NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
            psellipse(KOEC)(FOEC)}%
            }

            NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
            psellipse(KOEO)(FOEO)}%
            }

            NewDocumentCommand{EndeEllipsen}{sm}{%
            EreignisOmega%
            pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
            pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
            EreignisA
            EreignisB
            EreignisC
            rput[t](E){#2}%
            IfBooleanF{#1}{%
            rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
            rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
            rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
            rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
            }%
            }

            NewDocumentCommand{codeclip}{m}{%
            pscustom[linestyle=none]{%
            code{/clip /eoclip load def}%
            psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
            #1
            }%
            }

            %ExplSyntaxOn
            NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisOmega*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIII}{!O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisB*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
            psclip{EreignisB}%
            psclip{EreignisC}%
            EreignisA*[#1][#2]%
            endpsclip
            endpsclip
            }

            NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisA
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }
            %ExplSyntaxOff

            NewDocumentCommand{VIIIarea}{O{cyan}O{0.8}m}{%
            xintifboolexpr{#3=1}{arealI[#1][#2]}{}%
            xintifboolexpr{#3=2}{arealII[#1][#2]}{}%
            xintifboolexpr{#3=3}{arealIII[#1][#2]}{}%
            xintifboolexpr{#3=4}{arealIV[#1][#2]}{}%
            xintifboolexpr{#3=5}{arealV[#1][#2]}{}%
            xintifboolexpr{#3=6}{arealVI[#1][#2]}{}%
            xintifboolexpr{#3=7}{arealVII[#1][#2]}{}%
            xintifboolexpr{#3=8}{arealVIII[#1][#2]}{}%
            }

            NewDocumentCommand{VennIII}{oD(){0.8}m!g}{%
            IfValueTF{#1}%
            {%
            xintFor ##1 in {#3}do {VIIIarea[#1][#2]{##1}}%
            }%
            {%
            xintForpair ##1##2 in {#3}do {VIIIarea[##2][#2]{##1}}%
            }%
            EndeEllipsen{IfValueT{#4}{#4}}%
            }

            begin{document}

            begin{pspicture}(0,-1)(5,4)
            VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[orange]{6}{$Acap Bcap C$}%
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[cyan]{3,5,6}{$Acap (Bcup C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[magenta](0.5){1,5,6,7}{$(overline{A}cap overline{B})cup C$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[green](0.2){1,4,8}{$overline{A}setminus (Bcap C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[cyan]{8}{$(overline{A}setminus B)cap C$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII(1){(2,cyan),(5,orange),(6,green),(7,magenta)}{$(Asetminus B)cup (Bcap C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[cyan]{3,5}{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
            end{pspicture}


            end{document}


            enter image description here






            share|improve this answer























            • Hey bro, is there a shorter way? Your code seem being enormously complex.
              – chishimotoji
              Dec 1 at 10:48










            • This is because I first create all sorts of single surfaces by clipping. Then you can get any desired combination by fading in this area. This is a bit dull, but much easier to use. For example for area 2, area 4 and area 8you can use begin{pspicture}[shift=-4](0,-1)(5,4) arealI arealIV arealVIII EndeEllipsen{$overline{A}setminus (Bcap C)$} end{pspicture}
              – Thomas
              Dec 1 at 13:45


















            8














            With this definitions every surface can be colored.



            documentclass[pstricks]{standalone}
            usepackage{pst-node}
            usepackage{xparse,xintexpr}

            defradiusK{xinttheiexpr[6] 2*sqrt(3)/3relax}

            defKOEA{2.5,2}
            defFOEA{radiusK,radiusK}

            defKOEB{2,1}
            defFOEB{radiusK,radiusK}

            defKOEC{3,1}
            defFOEC{radiusK,radiusK}

            defKOEO{2.5,1.375}
            defFOEO{2.5,2.5}

            %uncomment the following lines to have ellipses
            %defKOEA{1.9,2.2}
            %defFOEA{1.4,1}
            %
            %defKOEB{3.3,2.2}
            %defFOEB{1.2,1}
            %
            %defKOEC{2.75,1.4}
            %defFOEC{1.4,1}
            %
            %defKOEO{2.5,2}
            %defFOEO{2.5,2.0}

            NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
            psellipse(KOEA)(FOEA)}%
            }

            NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
            psellipse(KOEB)(FOEB)}%
            }

            NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
            psellipse(KOEC)(FOEC)}%
            }

            NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
            psellipse(KOEO)(FOEO)}%
            }

            NewDocumentCommand{EndeEllipsen}{sm}{%
            EreignisOmega%
            pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
            pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
            EreignisA
            EreignisB
            EreignisC
            rput[t](E){#2}%
            IfBooleanF{#1}{%
            rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
            rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
            rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
            rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
            }%
            }

            NewDocumentCommand{codeclip}{m}{%
            pscustom[linestyle=none]{%
            code{/clip /eoclip load def}%
            psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
            #1
            }%
            }

            NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisOmega*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisB*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
            psclip{EreignisB}
            psclip{EreignisC}%
            EreignisA*[#1][#2]%
            endpsclip
            endpsclip
            }

            NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisA
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }

            begin{document}


            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            EndeEllipsen*{$Asetminus C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealVI
            EndeEllipsen*{$Acap Bcap C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealIII
            arealV
            arealVI
            EndeEllipsen*{$Acap (Bcup C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            EreignisC*%
            EndeEllipsen*{$(overline{A}cap overline{B})cup C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            arealIV
            arealVIII
            EndeEllipsen*{$overline{A}setminus (Bcap C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealVIII
            EndeEllipsen*{$(overline{A}setminus B)cap C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealII
            arealV
            arealVI
            arealVII
            EndeEllipsen*{$(Asetminus B)cup (Bcap C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealIII
            arealV
            EndeEllipsen*{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
            end{pspicture}


            end{document}




            Perhaps you want to check out this.



            documentclass[pstricks]{standalone}
            usepackage{pst-node}
            usepackage{xparse,xintexpr}

            %defradiusK{xinttheiexpr[6] 2*sqrt(3)/3relax}
            %
            %defKOEA{2.5,2}
            %defFOEA{radiusK,radiusK}
            %
            %defKOEB{2,1}
            %defFOEB{radiusK,radiusK}
            %
            %defKOEC{3,1}
            %defFOEC{radiusK,radiusK}
            %
            %defKOEO{2.5,1.375}
            %defFOEO{2.5,2.5}

            %uncomment the following lines to have ellipses
            defKOEA{1.9,2.2}
            defFOEA{1.4,1}

            defKOEB{3.3,2.2}
            defFOEB{1.2,1}

            defKOEC{2.75,1.4}
            defFOEC{1.4,1}

            defKOEO{2.5,2}
            defFOEO{2.5,2.0}

            NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
            psellipse(KOEA)(FOEA)}%
            }

            NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
            psellipse(KOEB)(FOEB)}%
            }

            NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
            psellipse(KOEC)(FOEC)}%
            }

            NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
            psellipse(KOEO)(FOEO)}%
            }

            NewDocumentCommand{EndeEllipsen}{sm}{%
            EreignisOmega%
            pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
            pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
            EreignisA
            EreignisB
            EreignisC
            rput[t](E){#2}%
            IfBooleanF{#1}{%
            rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
            rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
            rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
            rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
            }%
            }

            NewDocumentCommand{codeclip}{m}{%
            pscustom[linestyle=none]{%
            code{/clip /eoclip load def}%
            psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
            #1
            }%
            }

            NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisOmega*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisB*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
            psclip{EreignisB}
            psclip{EreignisC}%
            EreignisA*[#1][#2]%
            endpsclip
            endpsclip
            }

            NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisA
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }

            begin{document}


            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            EndeEllipsen{$Asetminus C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealVI
            EndeEllipsen{$Acap Bcap C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealIII
            arealV
            arealVI
            EndeEllipsen{$Acap (Bcup C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            EreignisC*%
            EndeEllipsen{$(overline{A}cap overline{B})cup C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            arealIV
            arealVIII
            EndeEllipsen{$overline{A}setminus (Bcap C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealVIII
            EndeEllipsen{$(overline{A}setminus B)cap C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealII
            arealV
            arealVI
            arealVII
            EndeEllipsen{$(Asetminus B)cup (Bcap C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealIII
            arealV
            EndeEllipsen{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
            end{pspicture}


            end{document}




            With the help of xint-package using xintFor and xintForpair you can write



            VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%


            so every surface becomes an own color, or you write



            VennIII[blue](0.5){2,4,6,8}{Text}%


            and all becomes color blue with opacity 0.5.



            documentclass[pstricks]{standalone}
            usepackage{pst-node}
            usepackage{xparse,xintexpr}

            defKOEA{1.9,2.2}
            defFOEA{1.4,1}

            defKOEB{3.3,2.2}
            defFOEB{1.2,1}

            defKOEC{2.75,1.4}
            defFOEC{1.4,1}

            defKOEO{2.5,2}
            defFOEO{2.5,2.0}

            NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
            psellipse(KOEA)(FOEA)}%
            }

            NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
            psellipse(KOEB)(FOEB)}%
            }

            NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
            psellipse(KOEC)(FOEC)}%
            }

            NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
            psellipse(KOEO)(FOEO)}%
            }

            NewDocumentCommand{EndeEllipsen}{sm}{%
            EreignisOmega%
            pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
            pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
            EreignisA
            EreignisB
            EreignisC
            rput[t](E){#2}%
            IfBooleanF{#1}{%
            rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
            rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
            rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
            rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
            }%
            }

            NewDocumentCommand{codeclip}{m}{%
            pscustom[linestyle=none]{%
            code{/clip /eoclip load def}%
            psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
            #1
            }%
            }

            %ExplSyntaxOn
            NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisOmega*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIII}{!O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisB*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
            psclip{EreignisB}%
            psclip{EreignisC}%
            EreignisA*[#1][#2]%
            endpsclip
            endpsclip
            }

            NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisA
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }
            %ExplSyntaxOff

            NewDocumentCommand{VIIIarea}{O{cyan}O{0.8}m}{%
            xintifboolexpr{#3=1}{arealI[#1][#2]}{}%
            xintifboolexpr{#3=2}{arealII[#1][#2]}{}%
            xintifboolexpr{#3=3}{arealIII[#1][#2]}{}%
            xintifboolexpr{#3=4}{arealIV[#1][#2]}{}%
            xintifboolexpr{#3=5}{arealV[#1][#2]}{}%
            xintifboolexpr{#3=6}{arealVI[#1][#2]}{}%
            xintifboolexpr{#3=7}{arealVII[#1][#2]}{}%
            xintifboolexpr{#3=8}{arealVIII[#1][#2]}{}%
            }

            NewDocumentCommand{VennIII}{oD(){0.8}m!g}{%
            IfValueTF{#1}%
            {%
            xintFor ##1 in {#3}do {VIIIarea[#1][#2]{##1}}%
            }%
            {%
            xintForpair ##1##2 in {#3}do {VIIIarea[##2][#2]{##1}}%
            }%
            EndeEllipsen{IfValueT{#4}{#4}}%
            }

            begin{document}

            begin{pspicture}(0,-1)(5,4)
            VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[orange]{6}{$Acap Bcap C$}%
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[cyan]{3,5,6}{$Acap (Bcup C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[magenta](0.5){1,5,6,7}{$(overline{A}cap overline{B})cup C$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[green](0.2){1,4,8}{$overline{A}setminus (Bcap C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[cyan]{8}{$(overline{A}setminus B)cap C$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII(1){(2,cyan),(5,orange),(6,green),(7,magenta)}{$(Asetminus B)cup (Bcap C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[cyan]{3,5}{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
            end{pspicture}


            end{document}


            enter image description here






            share|improve this answer























            • Hey bro, is there a shorter way? Your code seem being enormously complex.
              – chishimotoji
              Dec 1 at 10:48










            • This is because I first create all sorts of single surfaces by clipping. Then you can get any desired combination by fading in this area. This is a bit dull, but much easier to use. For example for area 2, area 4 and area 8you can use begin{pspicture}[shift=-4](0,-1)(5,4) arealI arealIV arealVIII EndeEllipsen{$overline{A}setminus (Bcap C)$} end{pspicture}
              – Thomas
              Dec 1 at 13:45
















            8












            8








            8






            With this definitions every surface can be colored.



            documentclass[pstricks]{standalone}
            usepackage{pst-node}
            usepackage{xparse,xintexpr}

            defradiusK{xinttheiexpr[6] 2*sqrt(3)/3relax}

            defKOEA{2.5,2}
            defFOEA{radiusK,radiusK}

            defKOEB{2,1}
            defFOEB{radiusK,radiusK}

            defKOEC{3,1}
            defFOEC{radiusK,radiusK}

            defKOEO{2.5,1.375}
            defFOEO{2.5,2.5}

            %uncomment the following lines to have ellipses
            %defKOEA{1.9,2.2}
            %defFOEA{1.4,1}
            %
            %defKOEB{3.3,2.2}
            %defFOEB{1.2,1}
            %
            %defKOEC{2.75,1.4}
            %defFOEC{1.4,1}
            %
            %defKOEO{2.5,2}
            %defFOEO{2.5,2.0}

            NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
            psellipse(KOEA)(FOEA)}%
            }

            NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
            psellipse(KOEB)(FOEB)}%
            }

            NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
            psellipse(KOEC)(FOEC)}%
            }

            NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
            psellipse(KOEO)(FOEO)}%
            }

            NewDocumentCommand{EndeEllipsen}{sm}{%
            EreignisOmega%
            pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
            pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
            EreignisA
            EreignisB
            EreignisC
            rput[t](E){#2}%
            IfBooleanF{#1}{%
            rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
            rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
            rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
            rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
            }%
            }

            NewDocumentCommand{codeclip}{m}{%
            pscustom[linestyle=none]{%
            code{/clip /eoclip load def}%
            psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
            #1
            }%
            }

            NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisOmega*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisB*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
            psclip{EreignisB}
            psclip{EreignisC}%
            EreignisA*[#1][#2]%
            endpsclip
            endpsclip
            }

            NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisA
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }

            begin{document}


            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            EndeEllipsen*{$Asetminus C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealVI
            EndeEllipsen*{$Acap Bcap C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealIII
            arealV
            arealVI
            EndeEllipsen*{$Acap (Bcup C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            EreignisC*%
            EndeEllipsen*{$(overline{A}cap overline{B})cup C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            arealIV
            arealVIII
            EndeEllipsen*{$overline{A}setminus (Bcap C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealVIII
            EndeEllipsen*{$(overline{A}setminus B)cap C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealII
            arealV
            arealVI
            arealVII
            EndeEllipsen*{$(Asetminus B)cup (Bcap C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealIII
            arealV
            EndeEllipsen*{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
            end{pspicture}


            end{document}




            Perhaps you want to check out this.



            documentclass[pstricks]{standalone}
            usepackage{pst-node}
            usepackage{xparse,xintexpr}

            %defradiusK{xinttheiexpr[6] 2*sqrt(3)/3relax}
            %
            %defKOEA{2.5,2}
            %defFOEA{radiusK,radiusK}
            %
            %defKOEB{2,1}
            %defFOEB{radiusK,radiusK}
            %
            %defKOEC{3,1}
            %defFOEC{radiusK,radiusK}
            %
            %defKOEO{2.5,1.375}
            %defFOEO{2.5,2.5}

            %uncomment the following lines to have ellipses
            defKOEA{1.9,2.2}
            defFOEA{1.4,1}

            defKOEB{3.3,2.2}
            defFOEB{1.2,1}

            defKOEC{2.75,1.4}
            defFOEC{1.4,1}

            defKOEO{2.5,2}
            defFOEO{2.5,2.0}

            NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
            psellipse(KOEA)(FOEA)}%
            }

            NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
            psellipse(KOEB)(FOEB)}%
            }

            NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
            psellipse(KOEC)(FOEC)}%
            }

            NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
            psellipse(KOEO)(FOEO)}%
            }

            NewDocumentCommand{EndeEllipsen}{sm}{%
            EreignisOmega%
            pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
            pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
            EreignisA
            EreignisB
            EreignisC
            rput[t](E){#2}%
            IfBooleanF{#1}{%
            rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
            rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
            rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
            rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
            }%
            }

            NewDocumentCommand{codeclip}{m}{%
            pscustom[linestyle=none]{%
            code{/clip /eoclip load def}%
            psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
            #1
            }%
            }

            NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisOmega*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisB*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
            psclip{EreignisB}
            psclip{EreignisC}%
            EreignisA*[#1][#2]%
            endpsclip
            endpsclip
            }

            NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisA
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }

            begin{document}


            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            EndeEllipsen{$Asetminus C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealVI
            EndeEllipsen{$Acap Bcap C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealIII
            arealV
            arealVI
            EndeEllipsen{$Acap (Bcup C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            EreignisC*%
            EndeEllipsen{$(overline{A}cap overline{B})cup C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            arealIV
            arealVIII
            EndeEllipsen{$overline{A}setminus (Bcap C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealVIII
            EndeEllipsen{$(overline{A}setminus B)cap C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealII
            arealV
            arealVI
            arealVII
            EndeEllipsen{$(Asetminus B)cup (Bcap C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealIII
            arealV
            EndeEllipsen{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
            end{pspicture}


            end{document}




            With the help of xint-package using xintFor and xintForpair you can write



            VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%


            so every surface becomes an own color, or you write



            VennIII[blue](0.5){2,4,6,8}{Text}%


            and all becomes color blue with opacity 0.5.



            documentclass[pstricks]{standalone}
            usepackage{pst-node}
            usepackage{xparse,xintexpr}

            defKOEA{1.9,2.2}
            defFOEA{1.4,1}

            defKOEB{3.3,2.2}
            defFOEB{1.2,1}

            defKOEC{2.75,1.4}
            defFOEC{1.4,1}

            defKOEO{2.5,2}
            defFOEO{2.5,2.0}

            NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
            psellipse(KOEA)(FOEA)}%
            }

            NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
            psellipse(KOEB)(FOEB)}%
            }

            NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
            psellipse(KOEC)(FOEC)}%
            }

            NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
            psellipse(KOEO)(FOEO)}%
            }

            NewDocumentCommand{EndeEllipsen}{sm}{%
            EreignisOmega%
            pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
            pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
            EreignisA
            EreignisB
            EreignisC
            rput[t](E){#2}%
            IfBooleanF{#1}{%
            rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
            rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
            rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
            rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
            }%
            }

            NewDocumentCommand{codeclip}{m}{%
            pscustom[linestyle=none]{%
            code{/clip /eoclip load def}%
            psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
            #1
            }%
            }

            %ExplSyntaxOn
            NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisOmega*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIII}{!O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisB*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
            psclip{EreignisB}%
            psclip{EreignisC}%
            EreignisA*[#1][#2]%
            endpsclip
            endpsclip
            }

            NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisA
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }
            %ExplSyntaxOff

            NewDocumentCommand{VIIIarea}{O{cyan}O{0.8}m}{%
            xintifboolexpr{#3=1}{arealI[#1][#2]}{}%
            xintifboolexpr{#3=2}{arealII[#1][#2]}{}%
            xintifboolexpr{#3=3}{arealIII[#1][#2]}{}%
            xintifboolexpr{#3=4}{arealIV[#1][#2]}{}%
            xintifboolexpr{#3=5}{arealV[#1][#2]}{}%
            xintifboolexpr{#3=6}{arealVI[#1][#2]}{}%
            xintifboolexpr{#3=7}{arealVII[#1][#2]}{}%
            xintifboolexpr{#3=8}{arealVIII[#1][#2]}{}%
            }

            NewDocumentCommand{VennIII}{oD(){0.8}m!g}{%
            IfValueTF{#1}%
            {%
            xintFor ##1 in {#3}do {VIIIarea[#1][#2]{##1}}%
            }%
            {%
            xintForpair ##1##2 in {#3}do {VIIIarea[##2][#2]{##1}}%
            }%
            EndeEllipsen{IfValueT{#4}{#4}}%
            }

            begin{document}

            begin{pspicture}(0,-1)(5,4)
            VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[orange]{6}{$Acap Bcap C$}%
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[cyan]{3,5,6}{$Acap (Bcup C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[magenta](0.5){1,5,6,7}{$(overline{A}cap overline{B})cup C$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[green](0.2){1,4,8}{$overline{A}setminus (Bcap C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[cyan]{8}{$(overline{A}setminus B)cap C$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII(1){(2,cyan),(5,orange),(6,green),(7,magenta)}{$(Asetminus B)cup (Bcap C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[cyan]{3,5}{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
            end{pspicture}


            end{document}


            enter image description here






            share|improve this answer














            With this definitions every surface can be colored.



            documentclass[pstricks]{standalone}
            usepackage{pst-node}
            usepackage{xparse,xintexpr}

            defradiusK{xinttheiexpr[6] 2*sqrt(3)/3relax}

            defKOEA{2.5,2}
            defFOEA{radiusK,radiusK}

            defKOEB{2,1}
            defFOEB{radiusK,radiusK}

            defKOEC{3,1}
            defFOEC{radiusK,radiusK}

            defKOEO{2.5,1.375}
            defFOEO{2.5,2.5}

            %uncomment the following lines to have ellipses
            %defKOEA{1.9,2.2}
            %defFOEA{1.4,1}
            %
            %defKOEB{3.3,2.2}
            %defFOEB{1.2,1}
            %
            %defKOEC{2.75,1.4}
            %defFOEC{1.4,1}
            %
            %defKOEO{2.5,2}
            %defFOEO{2.5,2.0}

            NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
            psellipse(KOEA)(FOEA)}%
            }

            NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
            psellipse(KOEB)(FOEB)}%
            }

            NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
            psellipse(KOEC)(FOEC)}%
            }

            NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
            psellipse(KOEO)(FOEO)}%
            }

            NewDocumentCommand{EndeEllipsen}{sm}{%
            EreignisOmega%
            pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
            pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
            EreignisA
            EreignisB
            EreignisC
            rput[t](E){#2}%
            IfBooleanF{#1}{%
            rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
            rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
            rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
            rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
            }%
            }

            NewDocumentCommand{codeclip}{m}{%
            pscustom[linestyle=none]{%
            code{/clip /eoclip load def}%
            psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
            #1
            }%
            }

            NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisOmega*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisB*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
            psclip{EreignisB}
            psclip{EreignisC}%
            EreignisA*[#1][#2]%
            endpsclip
            endpsclip
            }

            NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisA
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }

            begin{document}


            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            EndeEllipsen*{$Asetminus C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealVI
            EndeEllipsen*{$Acap Bcap C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealIII
            arealV
            arealVI
            EndeEllipsen*{$Acap (Bcup C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            EreignisC*%
            EndeEllipsen*{$(overline{A}cap overline{B})cup C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            arealIV
            arealVIII
            EndeEllipsen*{$overline{A}setminus (Bcap C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealVIII
            EndeEllipsen*{$(overline{A}setminus B)cap C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealII
            arealV
            arealVI
            arealVII
            EndeEllipsen*{$(Asetminus B)cup (Bcap C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealIII
            arealV
            EndeEllipsen*{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
            end{pspicture}


            end{document}




            Perhaps you want to check out this.



            documentclass[pstricks]{standalone}
            usepackage{pst-node}
            usepackage{xparse,xintexpr}

            %defradiusK{xinttheiexpr[6] 2*sqrt(3)/3relax}
            %
            %defKOEA{2.5,2}
            %defFOEA{radiusK,radiusK}
            %
            %defKOEB{2,1}
            %defFOEB{radiusK,radiusK}
            %
            %defKOEC{3,1}
            %defFOEC{radiusK,radiusK}
            %
            %defKOEO{2.5,1.375}
            %defFOEO{2.5,2.5}

            %uncomment the following lines to have ellipses
            defKOEA{1.9,2.2}
            defFOEA{1.4,1}

            defKOEB{3.3,2.2}
            defFOEB{1.2,1}

            defKOEC{2.75,1.4}
            defFOEC{1.4,1}

            defKOEO{2.5,2}
            defFOEO{2.5,2.0}

            NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
            psellipse(KOEA)(FOEA)}%
            }

            NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
            psellipse(KOEB)(FOEB)}%
            }

            NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
            psellipse(KOEC)(FOEC)}%
            }

            NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
            psellipse(KOEO)(FOEO)}%
            }

            NewDocumentCommand{EndeEllipsen}{sm}{%
            EreignisOmega%
            pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
            pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
            EreignisA
            EreignisB
            EreignisC
            rput[t](E){#2}%
            IfBooleanF{#1}{%
            rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
            rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
            rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
            rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
            }%
            }

            NewDocumentCommand{codeclip}{m}{%
            pscustom[linestyle=none]{%
            code{/clip /eoclip load def}%
            psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
            #1
            }%
            }

            NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisOmega*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisB*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
            psclip{EreignisB}
            psclip{EreignisC}%
            EreignisA*[#1][#2]%
            endpsclip
            endpsclip
            }

            NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisA
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }

            begin{document}


            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            EndeEllipsen{$Asetminus C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealVI
            EndeEllipsen{$Acap Bcap C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealIII
            arealV
            arealVI
            EndeEllipsen{$Acap (Bcup C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            EreignisC*%
            EndeEllipsen{$(overline{A}cap overline{B})cup C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealI
            arealIV
            arealVIII
            EndeEllipsen{$overline{A}setminus (Bcap C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealVIII
            EndeEllipsen{$(overline{A}setminus B)cap C$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealII
            arealV
            arealVI
            arealVII
            EndeEllipsen{$(Asetminus B)cup (Bcap C)$}
            end{pspicture}

            begin{pspicture}[shift=-4](0,-1)(5,4)
            arealIII
            arealV
            EndeEllipsen{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
            end{pspicture}


            end{document}




            With the help of xint-package using xintFor and xintForpair you can write



            VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%


            so every surface becomes an own color, or you write



            VennIII[blue](0.5){2,4,6,8}{Text}%


            and all becomes color blue with opacity 0.5.



            documentclass[pstricks]{standalone}
            usepackage{pst-node}
            usepackage{xparse,xintexpr}

            defKOEA{1.9,2.2}
            defFOEA{1.4,1}

            defKOEB{3.3,2.2}
            defFOEB{1.2,1}

            defKOEC{2.75,1.4}
            defFOEC{1.4,1}

            defKOEO{2.5,2}
            defFOEO{2.5,2.0}

            NewDocumentCommand{EreignisA}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEA)(FOEA)}{%
            psellipse(KOEA)(FOEA)}%
            }

            NewDocumentCommand{EreignisB}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEB)(FOEB)}{%
            psellipse(KOEB)(FOEB)}%
            }

            NewDocumentCommand{EreignisC}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEC)(FOEC)}{%
            psellipse(KOEC)(FOEC)}%
            }

            NewDocumentCommand{EreignisOmega}{sO{cyan}!O{0.8}}{%
            IfBooleanTF{#1}{%
            psellipse[fillstyle=solid,fillcolor=#2,opacity=#3](KOEO)(FOEO)}{%
            psellipse(KOEO)(FOEO)}%
            }

            NewDocumentCommand{EndeEllipsen}{sm}{%
            EreignisOmega%
            pnodes(0.25,3.75){Omega}(0.25,0.25){A}(4.75,3.75){B}(4.75,0.25){C}(2.5,-0.5){E}
            pnodes(0.7,3.36){MOmega}(0.85,1.55){MA}(4,3){MB}(3.8,0.75){MC}
            EreignisA
            EreignisB
            EreignisC
            rput[t](E){#2}%
            IfBooleanF{#1}{%
            rput(Omega){$Omega$}pcline[nodesepA=0.25](Omega)(MOmega)
            rput(A){$A$}pcline[nodesepA=0.25](A)(MA)
            rput(B){$B$}pcline[nodesepA=0.25](B)(MB)
            rput(C){$C$}pcline[nodesepA=0.2](C)(MC)
            }%
            }

            NewDocumentCommand{codeclip}{m}{%
            pscustom[linestyle=none]{%
            code{/clip /eoclip load def}%
            psframe(-maxdimen,-maxdimen)(maxdimen,maxdimen)
            #1
            }%
            }

            %ExplSyntaxOn
            NewDocumentCommand{arealI}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            }%
            codeclip{%
            EreignisB
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisOmega*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIII}{!O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealIV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisC
            }%
            codeclip{%
            EreignisC
            }%
            }%
            EreignisB*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealV}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisA*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVI}{O{cyan}!O{0.8}}{%
            psclip{EreignisB}%
            psclip{EreignisC}%
            EreignisA*[#1][#2]%
            endpsclip
            endpsclip
            }

            NewDocumentCommand{arealVII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            EreignisC
            }%
            codeclip{%
            EreignisA
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }

            NewDocumentCommand{arealVIII}{O{cyan}!O{0.8}}{%
            psclip{%
            codeclip{%
            EreignisA
            EreignisB
            }%
            codeclip{%
            EreignisB
            }%
            }%
            EreignisC*[#1][#2]%
            endpsclip
            }
            %ExplSyntaxOff

            NewDocumentCommand{VIIIarea}{O{cyan}O{0.8}m}{%
            xintifboolexpr{#3=1}{arealI[#1][#2]}{}%
            xintifboolexpr{#3=2}{arealII[#1][#2]}{}%
            xintifboolexpr{#3=3}{arealIII[#1][#2]}{}%
            xintifboolexpr{#3=4}{arealIV[#1][#2]}{}%
            xintifboolexpr{#3=5}{arealV[#1][#2]}{}%
            xintifboolexpr{#3=6}{arealVI[#1][#2]}{}%
            xintifboolexpr{#3=7}{arealVII[#1][#2]}{}%
            xintifboolexpr{#3=8}{arealVIII[#1][#2]}{}%
            }

            NewDocumentCommand{VennIII}{oD(){0.8}m!g}{%
            IfValueTF{#1}%
            {%
            xintFor ##1 in {#3}do {VIIIarea[#1][#2]{##1}}%
            }%
            {%
            xintForpair ##1##2 in {#3}do {VIIIarea[##2][#2]{##1}}%
            }%
            EndeEllipsen{IfValueT{#4}{#4}}%
            }

            begin{document}

            begin{pspicture}(0,-1)(5,4)
            VennIII{(2,red),(4,cyan),(6,magenta),(8,green)}{Text}%
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[orange]{6}{$Acap Bcap C$}%
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[cyan]{3,5,6}{$Acap (Bcup C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[magenta](0.5){1,5,6,7}{$(overline{A}cap overline{B})cup C$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[green](0.2){1,4,8}{$overline{A}setminus (Bcap C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[cyan]{8}{$(overline{A}setminus B)cap C$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII(1){(2,cyan),(5,orange),(6,green),(7,magenta)}{$(Asetminus B)cup (Bcap C)$}
            end{pspicture}

            begin{pspicture}(0,-1)(5,4)
            VennIII[cyan]{3,5}{$bigl((Acap B)cup (Acap C)bigr)setminus(Acap Bcap C)$}
            end{pspicture}


            end{document}


            enter image description here







            share|improve this answer














            share|improve this answer



            share|improve this answer








            edited Dec 1 at 22:36

























            answered Dec 1 at 7:23









            Thomas

            694212




            694212












            • Hey bro, is there a shorter way? Your code seem being enormously complex.
              – chishimotoji
              Dec 1 at 10:48










            • This is because I first create all sorts of single surfaces by clipping. Then you can get any desired combination by fading in this area. This is a bit dull, but much easier to use. For example for area 2, area 4 and area 8you can use begin{pspicture}[shift=-4](0,-1)(5,4) arealI arealIV arealVIII EndeEllipsen{$overline{A}setminus (Bcap C)$} end{pspicture}
              – Thomas
              Dec 1 at 13:45




















            • Hey bro, is there a shorter way? Your code seem being enormously complex.
              – chishimotoji
              Dec 1 at 10:48










            • This is because I first create all sorts of single surfaces by clipping. Then you can get any desired combination by fading in this area. This is a bit dull, but much easier to use. For example for area 2, area 4 and area 8you can use begin{pspicture}[shift=-4](0,-1)(5,4) arealI arealIV arealVIII EndeEllipsen{$overline{A}setminus (Bcap C)$} end{pspicture}
              – Thomas
              Dec 1 at 13:45


















            Hey bro, is there a shorter way? Your code seem being enormously complex.
            – chishimotoji
            Dec 1 at 10:48




            Hey bro, is there a shorter way? Your code seem being enormously complex.
            – chishimotoji
            Dec 1 at 10:48












            This is because I first create all sorts of single surfaces by clipping. Then you can get any desired combination by fading in this area. This is a bit dull, but much easier to use. For example for area 2, area 4 and area 8you can use begin{pspicture}[shift=-4](0,-1)(5,4) arealI arealIV arealVIII EndeEllipsen{$overline{A}setminus (Bcap C)$} end{pspicture}
            – Thomas
            Dec 1 at 13:45






            This is because I first create all sorts of single surfaces by clipping. Then you can get any desired combination by fading in this area. This is a bit dull, but much easier to use. For example for area 2, area 4 and area 8you can use begin{pspicture}[shift=-4](0,-1)(5,4) arealI arealIV arealVIII EndeEllipsen{$overline{A}setminus (Bcap C)$} end{pspicture}
            – Thomas
            Dec 1 at 13:45




















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