How to Prove P(a) → ∀x(P(x) ∨ ¬(x = a)) using Natural DeductionUsing natural deduction rules give a formal proofIntroductory Natural Deduction QuestionProve A ∨ D from A ∨ (B ∧ C) and (¬ B ∨ ¬ C) ∨ D ( LPL Q6.26) without using --> or material implicationGiven P ∨ ¬ P prove (P → Q) → ((¬ P → Q) → Q) by natural deductionHow to prove ¬(p→q) ⊢ p &¬qDoes anyone have a proof checker they prefer using for modal logic?How do you prove law of excluded middle using tertium non datur?How to prove : (( P → Q ) ∨ ( Q → R )) by natural deductionHow to prove ‘∃xP(x)’ from ‘¬∀x(P(x)→Q(x))’How would i go about using natural deduction to prove this argument is valid?
Sums of two squares in arithmetic progressions
In Bayesian inference, why are some terms dropped from the posterior predictive?
Processor speed limited at 0.4 Ghz
Unlock My Phone! February 2018
My ex-girlfriend uses my Apple ID to log in to her iPad. Do I have to give her my Apple ID password to reset it?
Should I tell management that I intend to leave due to bad software development practices?
Finitely generated matrix groups whose eigenvalues are all algebraic
OP Amp not amplifying audio signal
What are the G forces leaving Earth orbit?
Is there a hemisphere-neutral way of specifying a season?
Is it possible to create a QR code using text?
What is an equivalently powerful replacement spell for the Yuan-Ti's Suggestion spell?
Does Dispel Magic work on Tiny Hut?
Do Iron Man suits sport waste management systems?
files created then deleted at every second in tmp directory
How can a day be of 24 hours?
How exploitable/balanced is this homebrew spell: Spell Permanency?
How does a dynamic QR code work?
Can someone clarify Hamming's notion of important problems in relation to modern academia?
How to enclose theorems and definition in rectangles?
Are British MPs missing the point, with these 'Indicative Votes'?
Partial fraction expansion confusion
Getting extremely large arrows with tikzcd
How to show a landlord what we have in savings?
How to Prove P(a) → ∀x(P(x) ∨ ¬(x = a)) using Natural Deduction
Using natural deduction rules give a formal proofIntroductory Natural Deduction QuestionProve A ∨ D from A ∨ (B ∧ C) and (¬ B ∨ ¬ C) ∨ D ( LPL Q6.26) without using --> or material implicationGiven P ∨ ¬ P prove (P → Q) → ((¬ P → Q) → Q) by natural deductionHow to prove ¬(p→q) ⊢ p &¬qDoes anyone have a proof checker they prefer using for modal logic?How do you prove law of excluded middle using tertium non datur?How to prove : (( P → Q ) ∨ ( Q → R )) by natural deductionHow to prove ‘∃xP(x)’ from ‘¬∀x(P(x)→Q(x))’How would i go about using natural deduction to prove this argument is valid?
How would a formal Fitch proof look like.
I am given P(a) → ∀x(P(x) ∨ ¬(x = a)) to prove using Natural Deduction of predicate logic.
I am confused on how to proceed with the proof.
Please advice me on how to go about with this.
Thanks in advance
logic proof fitch quantification
asked 2 hours ago
Moey mnmMoey mnm
16
New contributor
Moey mnm is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
How would a formal Fitch proof look like.
I am given P(a) → ∀x(P(x) ∨ ¬(x = a)) to prove using Natural Deduction of predicate logic.
I am confused on how to proceed with the proof.
Please advice me on how to go about with this.
Thanks in advance
logic proof fitch quantification
asked 2 hours ago
Moey mnmMoey mnm
16
New contributor
Moey mnm is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
How would a formal Fitch proof look like.
I am given P(a) → ∀x(P(x) ∨ ¬(x = a)) to prove using Natural Deduction of predicate logic.
I am confused on how to proceed with the proof.
Please advice me on how to go about with this.
Thanks in advance
logic proof fitch quantification
asked 2 hours ago
Moey mnmMoey mnm
16
New contributor
Moey mnm is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
How would a formal Fitch proof look like.
I am given P(a) → ∀x(P(x) ∨ ¬(x = a)) to prove using Natural Deduction of predicate logic.
I am confused on how to proceed with the proof.
Please advice me on how to go about with this.
Thanks in advance
logic proof fitch quantification
logic proof fitch quantification
asked 2 hours ago
Moey mnmMoey mnm
16
New contributor
Moey mnm is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 hours ago
Moey mnmMoey mnm
16
New contributor
Moey mnm is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 hours ago
Moey mnmMoey mnm
16
New contributor
Moey mnm is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 hours ago
Moey mnmMoey mnm
16
asked 2 hours ago
Moey mnmMoey mnm
16
16
New contributor
Moey mnm is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Moey mnm is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Moey mnm is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
HINT: I'll sketch the derivation. Since the theorem is a conditional, try using conditional proof/conditional-introduction by assuming P(a) and trying to derive ∀x(P(x) ∨ ¬(x = a)) from it. Here, to derive it, I would try an indirect proof by assuming the negation ¬∀x(P(x) ∨ ¬(x = a)) and trying to derive a contradiction. Use quantifier equivalence rules to get ∃x¬(P(x) ∨ ¬(x = a)).
The next steps will be a little different depending on your list of rules (quantifier rules typically come with restrictions to ensure the rules are sound, and different texts will use different restrictions). Roughly, we can let y be stand for the particular such that ¬(P(y) ∨ ¬(y = a)). Apply De Morgan's law to get ¬P(y) ∧ (y = a). Since y = a, it must be that ¬P(a), contradicting our assumption that P(a). Hence our contradiction completing the indirect proof of ∀x(P(x) ∨ ¬(x = a)).
Hope this helps!
answered 1 hour ago
AdamAdam
4358
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "265"
;
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: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
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
);
);
Moey mnm is a new contributor. Be nice, and check out our Code of Conduct.
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%2fphilosophy.stackexchange.com%2fquestions%2f61580%2fhow-to-prove-pa-%25e2%2586%2592-%25e2%2588%2580xpx-%25e2%2588%25a8-%25c2%25acx-a-using-natural-deduction%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
HINT: I'll sketch the derivation. Since the theorem is a conditional, try using conditional proof/conditional-introduction by assuming P(a) and trying to derive ∀x(P(x) ∨ ¬(x = a)) from it. Here, to derive it, I would try an indirect proof by assuming the negation ¬∀x(P(x) ∨ ¬(x = a)) and trying to derive a contradiction. Use quantifier equivalence rules to get ∃x¬(P(x) ∨ ¬(x = a)).
The next steps will be a little different depending on your list of rules (quantifier rules typically come with restrictions to ensure the rules are sound, and different texts will use different restrictions). Roughly, we can let y be stand for the particular such that ¬(P(y) ∨ ¬(y = a)). Apply De Morgan's law to get ¬P(y) ∧ (y = a). Since y = a, it must be that ¬P(a), contradicting our assumption that P(a). Hence our contradiction completing the indirect proof of ∀x(P(x) ∨ ¬(x = a)).
Hope this helps!
answered 1 hour ago
AdamAdam
4358
add a comment |
HINT: I'll sketch the derivation. Since the theorem is a conditional, try using conditional proof/conditional-introduction by assuming P(a) and trying to derive ∀x(P(x) ∨ ¬(x = a)) from it. Here, to derive it, I would try an indirect proof by assuming the negation ¬∀x(P(x) ∨ ¬(x = a)) and trying to derive a contradiction. Use quantifier equivalence rules to get ∃x¬(P(x) ∨ ¬(x = a)).
The next steps will be a little different depending on your list of rules (quantifier rules typically come with restrictions to ensure the rules are sound, and different texts will use different restrictions). Roughly, we can let y be stand for the particular such that ¬(P(y) ∨ ¬(y = a)). Apply De Morgan's law to get ¬P(y) ∧ (y = a). Since y = a, it must be that ¬P(a), contradicting our assumption that P(a). Hence our contradiction completing the indirect proof of ∀x(P(x) ∨ ¬(x = a)).
Hope this helps!
answered 1 hour ago
AdamAdam
4358
add a comment |
HINT: I'll sketch the derivation. Since the theorem is a conditional, try using conditional proof/conditional-introduction by assuming P(a) and trying to derive ∀x(P(x) ∨ ¬(x = a)) from it. Here, to derive it, I would try an indirect proof by assuming the negation ¬∀x(P(x) ∨ ¬(x = a)) and trying to derive a contradiction. Use quantifier equivalence rules to get ∃x¬(P(x) ∨ ¬(x = a)).
The next steps will be a little different depending on your list of rules (quantifier rules typically come with restrictions to ensure the rules are sound, and different texts will use different restrictions). Roughly, we can let y be stand for the particular such that ¬(P(y) ∨ ¬(y = a)). Apply De Morgan's law to get ¬P(y) ∧ (y = a). Since y = a, it must be that ¬P(a), contradicting our assumption that P(a). Hence our contradiction completing the indirect proof of ∀x(P(x) ∨ ¬(x = a)).
Hope this helps!
answered 1 hour ago
AdamAdam
4358
HINT: I'll sketch the derivation. Since the theorem is a conditional, try using conditional proof/conditional-introduction by assuming P(a) and trying to derive ∀x(P(x) ∨ ¬(x = a)) from it. Here, to derive it, I would try an indirect proof by assuming the negation ¬∀x(P(x) ∨ ¬(x = a)) and trying to derive a contradiction. Use quantifier equivalence rules to get ∃x¬(P(x) ∨ ¬(x = a)).
The next steps will be a little different depending on your list of rules (quantifier rules typically come with restrictions to ensure the rules are sound, and different texts will use different restrictions). Roughly, we can let y be stand for the particular such that ¬(P(y) ∨ ¬(y = a)). Apply De Morgan's law to get ¬P(y) ∧ (y = a). Since y = a, it must be that ¬P(a), contradicting our assumption that P(a). Hence our contradiction completing the indirect proof of ∀x(P(x) ∨ ¬(x = a)).
Hope this helps!
answered 1 hour ago
AdamAdam
4358
answered 1 hour ago
AdamAdam
4358
answered 1 hour ago
AdamAdam
4358
answered 1 hour ago
AdamAdam
4358
4358
add a comment |
add a comment |
Moey mnm is a new contributor. Be nice, and check out our Code of Conduct.
Moey mnm is a new contributor. Be nice, and check out our Code of Conduct.
Moey mnm is a new contributor. Be nice, and check out our Code of Conduct.
Moey mnm is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Philosophy 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.
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%2fphilosophy.stackexchange.com%2fquestions%2f61580%2fhow-to-prove-pa-%25e2%2586%2592-%25e2%2588%2580xpx-%25e2%2588%25a8-%25c2%25acx-a-using-natural-deduction%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
