# Tagged Questions

Questions about truth tables, conjunctive and disjunctive normal forms, negation, and implication of unquantified propositions would fit very nicely under this tag. Questions about other kind of logics should be tagged with [logic] instead.

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### Who is the culprit?

" Andy says: "Cindy is guilty". Bart says: "I am not guilty". Cindy says: "Danny is guilty". Danny says: "Cindy lies if she says I am guilty". We know there is exactly one guilty person and ...
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### Is this (tricky) natural deduction with De Morgan's laws correct?

Just a practice question, however just wondering if this ND proof is correct? I have put brackets in 2.2 and not in 2.3 however this shouldn't make a difference?
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### Prove that $K$ is finitely definable iff $K$ has finite support

Hi guys I need to prove a Finite Support Theorem which states that $K$ is finitely definable iff $K$ has finite support. Unfortunately I succeeded in proving only the first part of if and only if. ...
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### Did I solve a basic derivation problem correctly?

The following problem is from "mathematical logic" by ian chiswell and wilfrid hodges, 2007.
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I am learning to derive proofs of some sentences based on logical axiom schemes and inference rules. But there is a lot of unclear moments, like getting hypothesis. The one such example would be $A ... 0answers 34 views ### How to derive this equivalence in propositional logic (Xv!X)->(X->Z)v(Z->X) I have no special skills of doing this. Can you introduce how to think of that ? I could take Xv!X as hip and then proof by parts x -> (X->Z)v(Z->X). But is the best way always to split disjunction ... 1answer 45 views ### A formula$\phi$is logically equivalent to a another formula which contains only propositional variables and the connectives$\wedge$and$\to$Let$v_0$be the valuation that assigns true ($T$) to every propositional variable. I'm trying to show that any formula$\phi$is logically equivalent to one with only propositional variables and the ... 1answer 40 views ### What is the order of precedence to$\Gamma \vdash \phi \Rightarrow \psi$? In this context,$\phi$and$\psi$are formulas and$\Gamma$is a set of formulas. I'm not quite sure what it means. Does it mean$\Gamma \vdash (\phi \Rightarrow \psi)$or does it mean$(\Gamma ...
Does the following equivalence $$\lnot \lnot (A \lor B) \leftrightarrow (\lnot \lnot A \lor \lnot \lnot B)$$ hold in propositional intuitionistic logic? And in propositional minimal logic? (In ...