# Questions tagged [logic]

Questions about mathematical logic, including model theory, proof theory, computability theory (a.k.a. recursion theory), and non-standard logics. Questions which merely seek to apply logical or formal reasoning to other areas of mathematics should not use this tag. Consider using one of the following tags as well, if they fit the question: (model-theory), (set-theory), (computability), and (proof-theory). This tag is not for logical puzzles, use (puzzle).

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### Basic proof verification

Let $\alpha \in X$. I want to prove following statement $$\text{Condition } A(\alpha) \text{ is satisfied} \iff \text{Condition } B \text{ is satisified}.$$ First I assume that $\alpha \in X$ and ...
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### Fundamental axioms of logic used to interpret most of modern mathematics [duplicate]

so i'm going through Terrence Tao's analysis 1 and he has a clear emphasis on rigor, however its kind of a contradiction when he didn't even go over the basics of mathematical logic. A mathematical ...
19 views

### Distance, speed and time word problem. Calculate Time

A Business owner Alex, got a call for an urgent business meeting and he had to drive through a road which did not have network coverage. He immediately left in his Car driving at constant speed of 87 ...
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### What are the consequences of negating the Godel sentence in a formal system? [duplicate]

What is wrong with the following argument? Let $F = T + ¬G_T$, where $T$ is an effectively generated formal system and $G_T$ is its Godel sentence. Then, it is possible to prove within $F$ the First ...
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### Please criticize my attempted proof of a simple set theory lemma.

I am reading Terrence Tao's analysis 1 and am new to writing proofs. I'm currently financially unstable and have no one to talk about math's with, so any criticm would help me so much. In his book, I ...
23 views

### Problem about the Zhegalkin polynomial [closed]

Let the Zhegalkin polynomial for function 𝑓 consist of those and only those monomials that are not included in the polynomial for function 𝑔. How different can the functions 𝑓 and 𝑔 be? (Write the ...
9k views

### Help to understand material implication [closed]

This question comes from from my algebra paper: $(p \rightarrow q)$ is logically equivalent to ... (then four options are given). The module states that the correct option is $(\sim p \lor q)$. ...
1 vote
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### Why can't I prove the opposite expression the same way? [duplicate]

There's explanation in Tarski's book about belonging of the null class to every other class. It goes like this: “If x belongs to the null class, then x belongs to K. Whatever object we substitute here ...
1 vote
137 views

### Can someone explain how they derive a consequence from the axion of choice

To give you guys the context: This isn’t for anything specifically, however, I hear the phrase such and such “…then we invoke the axiom of choice…” or something like, “…but by the axiom of choice, we ...
401 views

### Need help with natural deduction logic proof (Chiswell/Hodge exercise 2.6.2d)

in Chiswell/Hodge exercisee 2.6.2d it asks for the proof of $\{\lnot(\phi\leftrightarrow\psi)\}\vdash((\lnot\phi)\leftrightarrow\psi)$. I've managed to produce half the proof, but I'm unable to ...
### Theorem derivations in truth functional logic - How do I formally prove $(\neg P \to Q) \to (P \lor Q)$ [closed]
$\forall x~(\lnot F(x)\to G(x))\to\forall x~(F(x)\vee G(x))$ I understand that $[\forall x~(\lnot F(x)\to G(x))]$ and $[\forall x~(F(x)\lor G(x))]$ are semantically the same, but I can't figure out ...