Give a categorical proof of p -> [q -> q] The 2019 Stack Overflow Developer Survey Results Are InFalse(ified) AxiomsHilbert calculus: Proof that every provable formula has a proofHelp with axiom in propositional logicWhy does adding material implication as an axiom to propositional calculus make every formula provable?$S5$ proof of $diamond square pto square p$Can someone break this Propositional logic formulae down for me via truth tableProof of $(neg A supset A) supset A$Can't seem to show that (P∧R)⇒¬(Q∧¬(P∧R)) is a tautologyUnderstanding of Material Implication$(p wedge q) wedge p$ convert to CNF
Time travel alters history but people keep saying nothing's changed
Patience, young "Padovan"
Geography at the pixel level
Deadlock Graph and Interpretation, solution to avoid
What are the motivations for publishing new editions of an existing textbook, beyond new discoveries in a field?
Is three citations per paragraph excessive for undergraduate research paper?
Idiomatic way to prevent slicing?
Carnot-Caratheodory metric
Inflated grade on resume at previous job, might former employer tell new employer?
Landlord wants to switch my lease to a "Land contract" to "get back at the city"
"What time...?" or "At what time...?" - what is more grammatically correct?
How to deal with fear of taking dependencies
Inversion Puzzle
Why don't Unix/Linux systems traverse through directories until they find the required version of a linked library?
aging parents with no investments
In microwave frequencies, do you use a circulator when you need a (near) perfect diode?
"To split hairs" vs "To be pedantic"
Is domain driven design an anti-SQL pattern?
How was Skylab's orbit inclination chosen?
Does a dangling wire really electrocute me if I'm standing in water?
Does it makes sense to buy a new cycle to learn riding?
How come people say “Would of”?
How to manage monthly salary
What do the Banks children have against barley water?
Give a categorical proof of p -> [q -> q]
The 2019 Stack Overflow Developer Survey Results Are InFalse(ified) AxiomsHilbert calculus: Proof that every provable formula has a proofHelp with axiom in propositional logicWhy does adding material implication as an axiom to propositional calculus make every formula provable?$S5$ proof of $diamond square pto square p$Can someone break this Propositional logic formulae down for me via truth tableProof of $(neg A supset A) supset A$Can't seem to show that (P∧R)⇒¬(Q∧¬(P∧R)) is a tautologyUnderstanding of Material Implication$(p wedge q) wedge p$ convert to CNF
$begingroup$
I am doing Fitch's Exercises of Symbolic Logic, Chapter 1. This is the first exercise. We have so far axioms such as the distributivity axiom, the axiom of conditioned repetition, the transitivity of implication. I really don't know how to show that this is a theorem.
logic propositional-calculus
edited Mar 23 at 4:27
MJD
47.8k29216397
asked Mar 23 at 3:59
simulacrasimulacra
463
$endgroup$
add a comment |
$begingroup$
I am doing Fitch's Exercises of Symbolic Logic, Chapter 1. This is the first exercise. We have so far axioms such as the distributivity axiom, the axiom of conditioned repetition, the transitivity of implication. I really don't know how to show that this is a theorem.
logic propositional-calculus
edited Mar 23 at 4:27
MJD
47.8k29216397
asked Mar 23 at 3:59
simulacrasimulacra
463
$endgroup$
add a comment |
$begingroup$
I am doing Fitch's Exercises of Symbolic Logic, Chapter 1. This is the first exercise. We have so far axioms such as the distributivity axiom, the axiom of conditioned repetition, the transitivity of implication. I really don't know how to show that this is a theorem.
logic propositional-calculus
edited Mar 23 at 4:27
MJD
47.8k29216397
asked Mar 23 at 3:59
simulacrasimulacra
463
$endgroup$
I am doing Fitch's Exercises of Symbolic Logic, Chapter 1. This is the first exercise. We have so far axioms such as the distributivity axiom, the axiom of conditioned repetition, the transitivity of implication. I really don't know how to show that this is a theorem.
logic propositional-calculus
logic propositional-calculus
edited Mar 23 at 4:27
MJD
47.8k29216397
asked Mar 23 at 3:59
simulacrasimulacra
463
edited Mar 23 at 4:27
MJD
47.8k29216397
asked Mar 23 at 3:59
simulacrasimulacra
463
edited Mar 23 at 4:27
MJD
47.8k29216397
edited Mar 23 at 4:27
MJD
47.8k29216397
edited Mar 23 at 4:27
MJD
47.8k29216397
47.8k29216397
asked Mar 23 at 3:59
simulacrasimulacra
463
asked Mar 23 at 3:59
simulacrasimulacra
463
asked Mar 23 at 3:59
simulacrasimulacra
463
463
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
thanks! I figured out that the proof looks like this (please note that I prove it like this because this is Chapter 1 and so all tools have not been given yet)
1) q->(q->q) axiom of conditioned repetition
2) q->(q->q)->q axiom of conditioned repetition
3) (q->(q->q))->(q->q) by 2 and distributivity
4) q->q by 1, 3, modus ponies
5) p->(q->q) axiom of conditioned repetition
answered Mar 23 at 7:09
simulacrasimulacra
463
$endgroup$
$begingroup$
modus ponies? $ddotsmile$
$endgroup$
– Graham Kemp
Mar 23 at 14:01
add a comment |
$begingroup$
Hint: If you can prove $r$, you can use $rto (pto r)$ to prove $pto r$;.
$endgroup$
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%2f3158937%2fgive-a-categorical-proof-of-p-q-q%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
thanks! I figured out that the proof looks like this (please note that I prove it like this because this is Chapter 1 and so all tools have not been given yet)
1) q->(q->q) axiom of conditioned repetition
2) q->(q->q)->q axiom of conditioned repetition
3) (q->(q->q))->(q->q) by 2 and distributivity
4) q->q by 1, 3, modus ponies
5) p->(q->q) axiom of conditioned repetition
answered Mar 23 at 7:09
simulacrasimulacra
463
$endgroup$
$begingroup$
modus ponies? $ddotsmile$
$endgroup$
– Graham Kemp
Mar 23 at 14:01
add a comment |
$begingroup$
thanks! I figured out that the proof looks like this (please note that I prove it like this because this is Chapter 1 and so all tools have not been given yet)
1) q->(q->q) axiom of conditioned repetition
2) q->(q->q)->q axiom of conditioned repetition
3) (q->(q->q))->(q->q) by 2 and distributivity
4) q->q by 1, 3, modus ponies
5) p->(q->q) axiom of conditioned repetition
answered Mar 23 at 7:09
simulacrasimulacra
463
$endgroup$
$begingroup$
modus ponies? $ddotsmile$
$endgroup$
– Graham Kemp
Mar 23 at 14:01
add a comment |
$begingroup$
thanks! I figured out that the proof looks like this (please note that I prove it like this because this is Chapter 1 and so all tools have not been given yet)
1) q->(q->q) axiom of conditioned repetition
2) q->(q->q)->q axiom of conditioned repetition
3) (q->(q->q))->(q->q) by 2 and distributivity
4) q->q by 1, 3, modus ponies
5) p->(q->q) axiom of conditioned repetition
answered Mar 23 at 7:09
simulacrasimulacra
463
$endgroup$
thanks! I figured out that the proof looks like this (please note that I prove it like this because this is Chapter 1 and so all tools have not been given yet)
1) q->(q->q) axiom of conditioned repetition
2) q->(q->q)->q axiom of conditioned repetition
3) (q->(q->q))->(q->q) by 2 and distributivity
4) q->q by 1, 3, modus ponies
5) p->(q->q) axiom of conditioned repetition
answered Mar 23 at 7:09
simulacrasimulacra
463
answered Mar 23 at 7:09
simulacrasimulacra
463
answered Mar 23 at 7:09
simulacrasimulacra
463
answered Mar 23 at 7:09
simulacrasimulacra
463
463
$begingroup$
modus ponies? $ddotsmile$
$endgroup$
– Graham Kemp
Mar 23 at 14:01
add a comment |
$begingroup$
modus ponies? $ddotsmile$
$endgroup$
– Graham Kemp
Mar 23 at 14:01
$begingroup$
modus ponies? $ddotsmile$
$endgroup$
– Graham Kemp
Mar 23 at 14:01
$begingroup$
modus ponies? $ddotsmile$
$endgroup$
– Graham Kemp
Mar 23 at 14:01
add a comment |
$begingroup$
Hint: If you can prove $r$, you can use $rto (pto r)$ to prove $pto r$;.
$endgroup$
add a comment |
$begingroup$
Hint: If you can prove $r$, you can use $rto (pto r)$ to prove $pto r$;.
$endgroup$
add a comment |
$begingroup$
Hint: If you can prove $r$, you can use $rto (pto r)$ to prove $pto r$;.
$endgroup$
Hint: If you can prove $r$, you can use $rto (pto r)$ to prove $pto r$;.
answered Mar 23 at 4:23
community wiki
MJD
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%2f3158937%2fgive-a-categorical-proof-of-p-q-q%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
