Is ${ emptyset }$ is a subset of set ${ emptyset, 1, 2, 3 }$?
$begingroup$
Is ${ emptyset }$ a subset of set ${ emptyset, 1, 2, 3 }$?
I know that empty set is subset of every set, but what about ${ emptyset }$? What if 'right set' was just ${1, 2, 3}$? Will it still be true that ${ emptyset }$ is a subset of set ${1, 2, 3}$?
discrete-mathematics elementary-set-theory
edited Dec 5 '18 at 15:37
Asaf Karagila♦
305k33435766
asked Dec 5 '18 at 15:28
Sergey MalinovSergey Malinov
174
$endgroup$
add a comment |
$begingroup$
Is ${ emptyset }$ a subset of set ${ emptyset, 1, 2, 3 }$?
I know that empty set is subset of every set, but what about ${ emptyset }$? What if 'right set' was just ${1, 2, 3}$? Will it still be true that ${ emptyset }$ is a subset of set ${1, 2, 3}$?
discrete-mathematics elementary-set-theory
edited Dec 5 '18 at 15:37
Asaf Karagila♦
305k33435766
asked Dec 5 '18 at 15:28
Sergey MalinovSergey Malinov
174
$endgroup$
$begingroup$
The set $A = { emptyset, 1, 2, 3 }$ has four elements. One of them is $emptyset$.
$endgroup$
– Mauro ALLEGRANZA
Dec 5 '18 at 15:30
1
$begingroup$
Correct : $emptyset$ is a subset of every set; thus $emptyset subseteq A$.
$endgroup$
– Mauro ALLEGRANZA
Dec 5 '18 at 15:31
$begingroup$
Now, the question is : is ${ emptyset } subseteq A$ ? We have to apply the def of subset ... or lists all the subsetts of $A$.
$endgroup$
– Mauro ALLEGRANZA
Dec 5 '18 at 15:32
$begingroup$
${emptyset}subseteq A$ if and only if $emptysetin A.$ (In general $Bsubseteq A$ if and only if every element of $B$ is an element of $A.$)
$endgroup$
– spaceisdarkgreen
Dec 5 '18 at 15:33
add a comment |
$begingroup$
Is ${ emptyset }$ a subset of set ${ emptyset, 1, 2, 3 }$?
I know that empty set is subset of every set, but what about ${ emptyset }$? What if 'right set' was just ${1, 2, 3}$? Will it still be true that ${ emptyset }$ is a subset of set ${1, 2, 3}$?
discrete-mathematics elementary-set-theory
edited Dec 5 '18 at 15:37
Asaf Karagila♦
305k33435766
asked Dec 5 '18 at 15:28
Sergey MalinovSergey Malinov
174
$endgroup$
Is ${ emptyset }$ a subset of set ${ emptyset, 1, 2, 3 }$?
I know that empty set is subset of every set, but what about ${ emptyset }$? What if 'right set' was just ${1, 2, 3}$? Will it still be true that ${ emptyset }$ is a subset of set ${1, 2, 3}$?
discrete-mathematics elementary-set-theory
discrete-mathematics elementary-set-theory
edited Dec 5 '18 at 15:37
Asaf Karagila♦
305k33435766
asked Dec 5 '18 at 15:28
Sergey MalinovSergey Malinov
174
edited Dec 5 '18 at 15:37
Asaf Karagila♦
305k33435766
asked Dec 5 '18 at 15:28
Sergey MalinovSergey Malinov
174
edited Dec 5 '18 at 15:37
Asaf Karagila♦
305k33435766
edited Dec 5 '18 at 15:37
Asaf Karagila♦
305k33435766
edited Dec 5 '18 at 15:37
Asaf Karagila♦
305k33435766
305k33435766
asked Dec 5 '18 at 15:28
Sergey MalinovSergey Malinov
174
asked Dec 5 '18 at 15:28
Sergey MalinovSergey Malinov
174
asked Dec 5 '18 at 15:28
Sergey MalinovSergey Malinov
174
174
$begingroup$
The set $A = { emptyset, 1, 2, 3 }$ has four elements. One of them is $emptyset$.
$endgroup$
– Mauro ALLEGRANZA
Dec 5 '18 at 15:30
1
$begingroup$
Correct : $emptyset$ is a subset of every set; thus $emptyset subseteq A$.
$endgroup$
– Mauro ALLEGRANZA
Dec 5 '18 at 15:31
$begingroup$
Now, the question is : is ${ emptyset } subseteq A$ ? We have to apply the def of subset ... or lists all the subsetts of $A$.
$endgroup$
– Mauro ALLEGRANZA
Dec 5 '18 at 15:32
$begingroup$
${emptyset}subseteq A$ if and only if $emptysetin A.$ (In general $Bsubseteq A$ if and only if every element of $B$ is an element of $A.$)
$endgroup$
– spaceisdarkgreen
Dec 5 '18 at 15:33
add a comment |
$begingroup$
The set $A = { emptyset, 1, 2, 3 }$ has four elements. One of them is $emptyset$.
$endgroup$
– Mauro ALLEGRANZA
Dec 5 '18 at 15:30
1
$begingroup$
Correct : $emptyset$ is a subset of every set; thus $emptyset subseteq A$.
$endgroup$
– Mauro ALLEGRANZA
Dec 5 '18 at 15:31
$begingroup$
Now, the question is : is ${ emptyset } subseteq A$ ? We have to apply the def of subset ... or lists all the subsetts of $A$.
$endgroup$
– Mauro ALLEGRANZA
Dec 5 '18 at 15:32
$begingroup$
${emptyset}subseteq A$ if and only if $emptysetin A.$ (In general $Bsubseteq A$ if and only if every element of $B$ is an element of $A.$)
$endgroup$
– spaceisdarkgreen
Dec 5 '18 at 15:33
$begingroup$
The set $A = { emptyset, 1, 2, 3 }$ has four elements. One of them is $emptyset$.
$endgroup$
– Mauro ALLEGRANZA
Dec 5 '18 at 15:30
$begingroup$
The set $A = { emptyset, 1, 2, 3 }$ has four elements. One of them is $emptyset$.
$endgroup$
– Mauro ALLEGRANZA
Dec 5 '18 at 15:30
1
1
$begingroup$
Correct : $emptyset$ is a subset of every set; thus $emptyset subseteq A$.
$endgroup$
– Mauro ALLEGRANZA
Dec 5 '18 at 15:31
$begingroup$
Correct : $emptyset$ is a subset of every set; thus $emptyset subseteq A$.
$endgroup$
– Mauro ALLEGRANZA
Dec 5 '18 at 15:31
$begingroup$
Now, the question is : is ${ emptyset } subseteq A$ ? We have to apply the def of subset ... or lists all the subsetts of $A$.
$endgroup$
– Mauro ALLEGRANZA
Dec 5 '18 at 15:32
$begingroup$
Now, the question is : is ${ emptyset } subseteq A$ ? We have to apply the def of subset ... or lists all the subsetts of $A$.
$endgroup$
– Mauro ALLEGRANZA
Dec 5 '18 at 15:32
$begingroup$
${emptyset}subseteq A$ if and only if $emptysetin A.$ (In general $Bsubseteq A$ if and only if every element of $B$ is an element of $A.$)
$endgroup$
– spaceisdarkgreen
Dec 5 '18 at 15:33
$begingroup$
${emptyset}subseteq A$ if and only if $emptysetin A.$ (In general $Bsubseteq A$ if and only if every element of $B$ is an element of $A.$)
$endgroup$
– spaceisdarkgreen
Dec 5 '18 at 15:33
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
The set ${x}$ is a subset of ${a,b,c}$ if and only if $x$ is equal to $a$, $b$ or $c$. So, unless you have a weird definition of $1$, $2$ or $3$, ${emptyset}nsubseteq{1,2,3}$. But ${emptyset}subseteq{emptyset, 1,2,3}$
Remark: The most usual construction of $Bbb N$ from ZFC defines $0=emptyset$ and $1={emptyset}$.
answered Dec 5 '18 at 15:33
ajotatxeajotatxe
53.9k24090
$endgroup$
add a comment |
$begingroup$
If you are asking about $emptyset$, then it is indeed the subset of any set.
If you are asking about $E = {emptyset, 1,2,3}$, then $emptyset in E$ and $emptyset subset E$.
Moreover, if $S = {emptyset}$ then $S subset E$.
answered Dec 5 '18 at 15:31
gt6989bgt6989b
34.6k22456
$endgroup$
2
$begingroup$
It looks to me like the question is asking whether ${varnothing}subseteq{varnothing,1,2,3}$, which is not what you're answering here.
$endgroup$
– Henning Makholm
Dec 5 '18 at 15:33
$begingroup$
@HenningMakholm OP changed the question twice, will redo
$endgroup$
– gt6989b
Dec 5 '18 at 15:34
add a comment |
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2 Answers
2
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oldest
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2 Answers
2
active
oldest
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$begingroup$
The set ${x}$ is a subset of ${a,b,c}$ if and only if $x$ is equal to $a$, $b$ or $c$. So, unless you have a weird definition of $1$, $2$ or $3$, ${emptyset}nsubseteq{1,2,3}$. But ${emptyset}subseteq{emptyset, 1,2,3}$
Remark: The most usual construction of $Bbb N$ from ZFC defines $0=emptyset$ and $1={emptyset}$.
answered Dec 5 '18 at 15:33
ajotatxeajotatxe
53.9k24090
$endgroup$
add a comment |
$begingroup$
The set ${x}$ is a subset of ${a,b,c}$ if and only if $x$ is equal to $a$, $b$ or $c$. So, unless you have a weird definition of $1$, $2$ or $3$, ${emptyset}nsubseteq{1,2,3}$. But ${emptyset}subseteq{emptyset, 1,2,3}$
Remark: The most usual construction of $Bbb N$ from ZFC defines $0=emptyset$ and $1={emptyset}$.
answered Dec 5 '18 at 15:33
ajotatxeajotatxe
53.9k24090
$endgroup$
add a comment |
$begingroup$
The set ${x}$ is a subset of ${a,b,c}$ if and only if $x$ is equal to $a$, $b$ or $c$. So, unless you have a weird definition of $1$, $2$ or $3$, ${emptyset}nsubseteq{1,2,3}$. But ${emptyset}subseteq{emptyset, 1,2,3}$
Remark: The most usual construction of $Bbb N$ from ZFC defines $0=emptyset$ and $1={emptyset}$.
answered Dec 5 '18 at 15:33
ajotatxeajotatxe
53.9k24090
$endgroup$
The set ${x}$ is a subset of ${a,b,c}$ if and only if $x$ is equal to $a$, $b$ or $c$. So, unless you have a weird definition of $1$, $2$ or $3$, ${emptyset}nsubseteq{1,2,3}$. But ${emptyset}subseteq{emptyset, 1,2,3}$
Remark: The most usual construction of $Bbb N$ from ZFC defines $0=emptyset$ and $1={emptyset}$.
answered Dec 5 '18 at 15:33
ajotatxeajotatxe
53.9k24090
edited Dec 5 '18 at 15:36
answered Dec 5 '18 at 15:33
ajotatxeajotatxe
53.9k24090
answered Dec 5 '18 at 15:33
ajotatxeajotatxe
53.9k24090
answered Dec 5 '18 at 15:33
ajotatxeajotatxe
53.9k24090
53.9k24090
add a comment |
add a comment |
$begingroup$
If you are asking about $emptyset$, then it is indeed the subset of any set.
If you are asking about $E = {emptyset, 1,2,3}$, then $emptyset in E$ and $emptyset subset E$.
Moreover, if $S = {emptyset}$ then $S subset E$.
answered Dec 5 '18 at 15:31
gt6989bgt6989b
34.6k22456
$endgroup$
2
$begingroup$
It looks to me like the question is asking whether ${varnothing}subseteq{varnothing,1,2,3}$, which is not what you're answering here.
$endgroup$
– Henning Makholm
Dec 5 '18 at 15:33
$begingroup$
@HenningMakholm OP changed the question twice, will redo
$endgroup$
– gt6989b
Dec 5 '18 at 15:34
add a comment |
$begingroup$
If you are asking about $emptyset$, then it is indeed the subset of any set.
If you are asking about $E = {emptyset, 1,2,3}$, then $emptyset in E$ and $emptyset subset E$.
Moreover, if $S = {emptyset}$ then $S subset E$.
answered Dec 5 '18 at 15:31
gt6989bgt6989b
34.6k22456
$endgroup$
2
$begingroup$
It looks to me like the question is asking whether ${varnothing}subseteq{varnothing,1,2,3}$, which is not what you're answering here.
$endgroup$
– Henning Makholm
Dec 5 '18 at 15:33
$begingroup$
@HenningMakholm OP changed the question twice, will redo
$endgroup$
– gt6989b
Dec 5 '18 at 15:34
add a comment |
$begingroup$
If you are asking about $emptyset$, then it is indeed the subset of any set.
If you are asking about $E = {emptyset, 1,2,3}$, then $emptyset in E$ and $emptyset subset E$.
Moreover, if $S = {emptyset}$ then $S subset E$.
answered Dec 5 '18 at 15:31
gt6989bgt6989b
34.6k22456
$endgroup$
If you are asking about $emptyset$, then it is indeed the subset of any set.
If you are asking about $E = {emptyset, 1,2,3}$, then $emptyset in E$ and $emptyset subset E$.
Moreover, if $S = {emptyset}$ then $S subset E$.
answered Dec 5 '18 at 15:31
gt6989bgt6989b
34.6k22456
edited Dec 5 '18 at 15:35
answered Dec 5 '18 at 15:31
gt6989bgt6989b
34.6k22456
answered Dec 5 '18 at 15:31
gt6989bgt6989b
34.6k22456
answered Dec 5 '18 at 15:31
gt6989bgt6989b
34.6k22456
34.6k22456
2
$begingroup$
It looks to me like the question is asking whether ${varnothing}subseteq{varnothing,1,2,3}$, which is not what you're answering here.
$endgroup$
– Henning Makholm
Dec 5 '18 at 15:33
$begingroup$
@HenningMakholm OP changed the question twice, will redo
$endgroup$
– gt6989b
Dec 5 '18 at 15:34
add a comment |
2
$begingroup$
It looks to me like the question is asking whether ${varnothing}subseteq{varnothing,1,2,3}$, which is not what you're answering here.
$endgroup$
– Henning Makholm
Dec 5 '18 at 15:33
$begingroup$
@HenningMakholm OP changed the question twice, will redo
$endgroup$
– gt6989b
Dec 5 '18 at 15:34
2
2
$begingroup$
It looks to me like the question is asking whether ${varnothing}subseteq{varnothing,1,2,3}$, which is not what you're answering here.
$endgroup$
– Henning Makholm
Dec 5 '18 at 15:33
$begingroup$
It looks to me like the question is asking whether ${varnothing}subseteq{varnothing,1,2,3}$, which is not what you're answering here.
$endgroup$
– Henning Makholm
Dec 5 '18 at 15:33
$begingroup$
@HenningMakholm OP changed the question twice, will redo
$endgroup$
– gt6989b
Dec 5 '18 at 15:34
$begingroup$
@HenningMakholm OP changed the question twice, will redo
$endgroup$
– gt6989b
Dec 5 '18 at 15:34
add a comment |
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$begingroup$
The set $A = { emptyset, 1, 2, 3 }$ has four elements. One of them is $emptyset$.
$endgroup$
– Mauro ALLEGRANZA
Dec 5 '18 at 15:30
1
$begingroup$
Correct : $emptyset$ is a subset of every set; thus $emptyset subseteq A$.
$endgroup$
– Mauro ALLEGRANZA
Dec 5 '18 at 15:31
$begingroup$
Now, the question is : is ${ emptyset } subseteq A$ ? We have to apply the def of subset ... or lists all the subsetts of $A$.
$endgroup$
– Mauro ALLEGRANZA
Dec 5 '18 at 15:32
$begingroup$
${emptyset}subseteq A$ if and only if $emptysetin A.$ (In general $Bsubseteq A$ if and only if every element of $B$ is an element of $A.$)
$endgroup$
– spaceisdarkgreen
Dec 5 '18 at 15:33