Prove p, assuming the following: (1) r → ¬q (2) q (3) ¬(p ∧ ¬s) ∧ (¬r → p)
$begingroup$
Prove p, assuming the following:
- (1) r → ¬q assumption
- (2) q assumption
- (3) ¬(p ∧ ¬s) ∧ (¬r → p) assumption
I need help after (4) not sure how to start this
(4) q → ¬r contrapostion (1)
(5)¬r modus ponens (2),(4)
(6)
(7)
discrete-mathematics propositional-calculus
asked Jan 24 at 16:38
Derek LongDerek Long
115
$endgroup$
add a comment |
$begingroup$
Prove p, assuming the following:
- (1) r → ¬q assumption
- (2) q assumption
- (3) ¬(p ∧ ¬s) ∧ (¬r → p) assumption
I need help after (4) not sure how to start this
(4) q → ¬r contrapostion (1)
(5)¬r modus ponens (2),(4)
(6)
(7)
discrete-mathematics propositional-calculus
asked Jan 24 at 16:38
Derek LongDerek Long
115
$endgroup$
$begingroup$
(4) is wrong....
$endgroup$
– Mauro ALLEGRANZA
Jan 24 at 16:45
$begingroup$
Use Contraposition on (1) to get $q to lnot r$. Then use MP with (2) to get $lnot r$.
$endgroup$
– Mauro ALLEGRANZA
Jan 24 at 16:46
add a comment |
$begingroup$
Prove p, assuming the following:
- (1) r → ¬q assumption
- (2) q assumption
- (3) ¬(p ∧ ¬s) ∧ (¬r → p) assumption
I need help after (4) not sure how to start this
(4) q → ¬r contrapostion (1)
(5)¬r modus ponens (2),(4)
(6)
(7)
discrete-mathematics propositional-calculus
asked Jan 24 at 16:38
Derek LongDerek Long
115
$endgroup$
Prove p, assuming the following:
- (1) r → ¬q assumption
- (2) q assumption
- (3) ¬(p ∧ ¬s) ∧ (¬r → p) assumption
I need help after (4) not sure how to start this
(4) q → ¬r contrapostion (1)
(5)¬r modus ponens (2),(4)
(6)
(7)
discrete-mathematics propositional-calculus
discrete-mathematics propositional-calculus
asked Jan 24 at 16:38
Derek LongDerek Long
115
asked Jan 24 at 16:38
Derek LongDerek Long
115
edited Jan 24 at 17:44
Derek Long
asked Jan 24 at 16:38
Derek LongDerek Long
115
asked Jan 24 at 16:38
Derek LongDerek Long
115
asked Jan 24 at 16:38
Derek LongDerek Long
115
115
$begingroup$
(4) is wrong....
$endgroup$
– Mauro ALLEGRANZA
Jan 24 at 16:45
$begingroup$
Use Contraposition on (1) to get $q to lnot r$. Then use MP with (2) to get $lnot r$.
$endgroup$
– Mauro ALLEGRANZA
Jan 24 at 16:46
add a comment |
$begingroup$
(4) is wrong....
$endgroup$
– Mauro ALLEGRANZA
Jan 24 at 16:45
$begingroup$
Use Contraposition on (1) to get $q to lnot r$. Then use MP with (2) to get $lnot r$.
$endgroup$
– Mauro ALLEGRANZA
Jan 24 at 16:46
$begingroup$
(4) is wrong....
$endgroup$
– Mauro ALLEGRANZA
Jan 24 at 16:45
$begingroup$
(4) is wrong....
$endgroup$
– Mauro ALLEGRANZA
Jan 24 at 16:45
$begingroup$
Use Contraposition on (1) to get $q to lnot r$. Then use MP with (2) to get $lnot r$.
$endgroup$
– Mauro ALLEGRANZA
Jan 24 at 16:46
$begingroup$
Use Contraposition on (1) to get $q to lnot r$. Then use MP with (2) to get $lnot r$.
$endgroup$
– Mauro ALLEGRANZA
Jan 24 at 16:46
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Prove p, assuming the following:
(1) r → ¬q assumption
(2) q assumption
(3) ¬(p ∧ ¬s) ∧ (¬r → p) assumption
I need help after (4) not sure how to start this
(4) q → ¬r contrapostion (1)
(5)¬r modus ponens (2),(4)
(6) p Modus ponens (3),(4)
I figured it out!
answered Jan 24 at 20:31
Derek LongDerek Long
115
$endgroup$
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%2f3086089%2fprove-p-assuming-the-following-1-r-%25e2%2586%2592-%25c2%25acq-2-q-3-%25c2%25acp-%25e2%2588%25a7-%25c2%25acs-%25e2%2588%25a7-%25c2%25acr-%25e2%2586%2592-p%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
$begingroup$
Prove p, assuming the following:
(1) r → ¬q assumption
(2) q assumption
(3) ¬(p ∧ ¬s) ∧ (¬r → p) assumption
I need help after (4) not sure how to start this
(4) q → ¬r contrapostion (1)
(5)¬r modus ponens (2),(4)
(6) p Modus ponens (3),(4)
I figured it out!
answered Jan 24 at 20:31
Derek LongDerek Long
115
$endgroup$
add a comment |
$begingroup$
Prove p, assuming the following:
(1) r → ¬q assumption
(2) q assumption
(3) ¬(p ∧ ¬s) ∧ (¬r → p) assumption
I need help after (4) not sure how to start this
(4) q → ¬r contrapostion (1)
(5)¬r modus ponens (2),(4)
(6) p Modus ponens (3),(4)
I figured it out!
answered Jan 24 at 20:31
Derek LongDerek Long
115
$endgroup$
add a comment |
$begingroup$
Prove p, assuming the following:
(1) r → ¬q assumption
(2) q assumption
(3) ¬(p ∧ ¬s) ∧ (¬r → p) assumption
I need help after (4) not sure how to start this
(4) q → ¬r contrapostion (1)
(5)¬r modus ponens (2),(4)
(6) p Modus ponens (3),(4)
I figured it out!
answered Jan 24 at 20:31
Derek LongDerek Long
115
$endgroup$
Prove p, assuming the following:
(1) r → ¬q assumption
(2) q assumption
(3) ¬(p ∧ ¬s) ∧ (¬r → p) assumption
I need help after (4) not sure how to start this
(4) q → ¬r contrapostion (1)
(5)¬r modus ponens (2),(4)
(6) p Modus ponens (3),(4)
I figured it out!
answered Jan 24 at 20:31
Derek LongDerek Long
115
answered Jan 24 at 20:31
Derek LongDerek Long
115
answered Jan 24 at 20:31
Derek LongDerek Long
115
answered Jan 24 at 20:31
Derek LongDerek Long
115
115
add a comment |
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%2f3086089%2fprove-p-assuming-the-following-1-r-%25e2%2586%2592-%25c2%25acq-2-q-3-%25c2%25acp-%25e2%2588%25a7-%25c2%25acs-%25e2%2588%25a7-%25c2%25acr-%25e2%2586%2592-p%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
$begingroup$
(4) is wrong....
$endgroup$
– Mauro ALLEGRANZA
Jan 24 at 16:45
$begingroup$
Use Contraposition on (1) to get $q to lnot r$. Then use MP with (2) to get $lnot r$.
$endgroup$
– Mauro ALLEGRANZA
Jan 24 at 16:46