Proving $forall x forall y Rxy therefore forall x forall y Ryx$.
$begingroup$
I have been having a hard time trying to understand how to prove the following proof:
$forall x forall y Rxy therefore forall x forall y Ryx$
What I have done so far is opened the 2 sub-proofs for the Universal Introduction of $x$ and $y$ and after the subproof of $y$ assume the negation of $Rxy$ and prove that a contradiction exist, however, that where I get stuck.
logic first-order-logic quantifiers
edited Dec 9 '18 at 4:36
dantopa
6,64942245
asked Dec 8 '18 at 20:07
Kevin RKevin R
142
$endgroup$
add a comment |
$begingroup$
I have been having a hard time trying to understand how to prove the following proof:
$forall x forall y Rxy therefore forall x forall y Ryx$
What I have done so far is opened the 2 sub-proofs for the Universal Introduction of $x$ and $y$ and after the subproof of $y$ assume the negation of $Rxy$ and prove that a contradiction exist, however, that where I get stuck.
logic first-order-logic quantifiers
edited Dec 9 '18 at 4:36
dantopa
6,64942245
asked Dec 8 '18 at 20:07
Kevin RKevin R
142
$endgroup$
2
$begingroup$
Please edit the question to include which axioms you are working with.
$endgroup$
– Shaun
Dec 8 '18 at 20:12
add a comment |
$begingroup$
I have been having a hard time trying to understand how to prove the following proof:
$forall x forall y Rxy therefore forall x forall y Ryx$
What I have done so far is opened the 2 sub-proofs for the Universal Introduction of $x$ and $y$ and after the subproof of $y$ assume the negation of $Rxy$ and prove that a contradiction exist, however, that where I get stuck.
logic first-order-logic quantifiers
edited Dec 9 '18 at 4:36
dantopa
6,64942245
asked Dec 8 '18 at 20:07
Kevin RKevin R
142
$endgroup$
I have been having a hard time trying to understand how to prove the following proof:
$forall x forall y Rxy therefore forall x forall y Ryx$
What I have done so far is opened the 2 sub-proofs for the Universal Introduction of $x$ and $y$ and after the subproof of $y$ assume the negation of $Rxy$ and prove that a contradiction exist, however, that where I get stuck.
logic first-order-logic quantifiers
logic first-order-logic quantifiers
edited Dec 9 '18 at 4:36
dantopa
6,64942245
asked Dec 8 '18 at 20:07
Kevin RKevin R
142
edited Dec 9 '18 at 4:36
dantopa
6,64942245
asked Dec 8 '18 at 20:07
Kevin RKevin R
142
edited Dec 9 '18 at 4:36
dantopa
6,64942245
edited Dec 9 '18 at 4:36
dantopa
6,64942245
edited Dec 9 '18 at 4:36
dantopa
6,64942245
6,64942245
asked Dec 8 '18 at 20:07
Kevin RKevin R
142
asked Dec 8 '18 at 20:07
Kevin RKevin R
142
asked Dec 8 '18 at 20:07
Kevin RKevin R
142
142
2
$begingroup$
Please edit the question to include which axioms you are working with.
$endgroup$
– Shaun
Dec 8 '18 at 20:12
add a comment |
2
$begingroup$
Please edit the question to include which axioms you are working with.
$endgroup$
– Shaun
Dec 8 '18 at 20:12
2
2
$begingroup$
Please edit the question to include which axioms you are working with.
$endgroup$
– Shaun
Dec 8 '18 at 20:12
$begingroup$
Please edit the question to include which axioms you are working with.
$endgroup$
– Shaun
Dec 8 '18 at 20:12
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
What I have done so far is opened the 2 sub-proofs for the Universal Introduction of x and y...
What you hav to do is :
1) $∀x∀yRxy$
2) $∀yRay$ --- by UI
3) $Rab$ --- by UI
4) $∀yRyb$ --- by UG
5) $∀x∀yRyx$ --- by UG.
answered Dec 8 '18 at 20:14
Mauro ALLEGRANZAMauro ALLEGRANZA
67.2k449115
$endgroup$
$begingroup$
Really...wow thank you so much
$endgroup$
– Kevin R
Dec 8 '18 at 20:16
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3031576%2fproving-forall-x-forall-y-rxy-therefore-forall-x-forall-y-ryx%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
What I have done so far is opened the 2 sub-proofs for the Universal Introduction of x and y...
What you hav to do is :
1) $∀x∀yRxy$
2) $∀yRay$ --- by UI
3) $Rab$ --- by UI
4) $∀yRyb$ --- by UG
5) $∀x∀yRyx$ --- by UG.
answered Dec 8 '18 at 20:14
Mauro ALLEGRANZAMauro ALLEGRANZA
67.2k449115
$endgroup$
$begingroup$
Really...wow thank you so much
$endgroup$
– Kevin R
Dec 8 '18 at 20:16
add a comment |
$begingroup$
What I have done so far is opened the 2 sub-proofs for the Universal Introduction of x and y...
What you hav to do is :
1) $∀x∀yRxy$
2) $∀yRay$ --- by UI
3) $Rab$ --- by UI
4) $∀yRyb$ --- by UG
5) $∀x∀yRyx$ --- by UG.
answered Dec 8 '18 at 20:14
Mauro ALLEGRANZAMauro ALLEGRANZA
67.2k449115
$endgroup$
$begingroup$
Really...wow thank you so much
$endgroup$
– Kevin R
Dec 8 '18 at 20:16
add a comment |
$begingroup$
What I have done so far is opened the 2 sub-proofs for the Universal Introduction of x and y...
What you hav to do is :
1) $∀x∀yRxy$
2) $∀yRay$ --- by UI
3) $Rab$ --- by UI
4) $∀yRyb$ --- by UG
5) $∀x∀yRyx$ --- by UG.
answered Dec 8 '18 at 20:14
Mauro ALLEGRANZAMauro ALLEGRANZA
67.2k449115
$endgroup$
What I have done so far is opened the 2 sub-proofs for the Universal Introduction of x and y...
What you hav to do is :
1) $∀x∀yRxy$
2) $∀yRay$ --- by UI
3) $Rab$ --- by UI
4) $∀yRyb$ --- by UG
5) $∀x∀yRyx$ --- by UG.
answered Dec 8 '18 at 20:14
Mauro ALLEGRANZAMauro ALLEGRANZA
67.2k449115
edited Dec 8 '18 at 20:17
answered Dec 8 '18 at 20:14
Mauro ALLEGRANZAMauro ALLEGRANZA
67.2k449115
answered Dec 8 '18 at 20:14
Mauro ALLEGRANZAMauro ALLEGRANZA
67.2k449115
answered Dec 8 '18 at 20:14
Mauro ALLEGRANZAMauro ALLEGRANZA
67.2k449115
67.2k449115
$begingroup$
Really...wow thank you so much
$endgroup$
– Kevin R
Dec 8 '18 at 20:16
add a comment |
$begingroup$
Really...wow thank you so much
$endgroup$
– Kevin R
Dec 8 '18 at 20:16
$begingroup$
Really...wow thank you so much
$endgroup$
– Kevin R
Dec 8 '18 at 20:16
$begingroup$
Really...wow thank you so much
$endgroup$
– Kevin R
Dec 8 '18 at 20:16
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3031576%2fproving-forall-x-forall-y-rxy-therefore-forall-x-forall-y-ryx%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
2
$begingroup$
Please edit the question to include which axioms you are working with.
$endgroup$
– Shaun
Dec 8 '18 at 20:12