List questions from propositional-calculus

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Explain why, if $P$ is equivalent to $Q$, then $\sim P$ is equivalent to $\sim Q$?

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The principle of structural induction in logic

Published on 10 Apr 2026 - 1:20

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If we have proved that $n$ cannot be greater than $9$, have we also proved that the most it can be is $9$?

Published on 19 Jun 2023 - 5:55

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Proving $\Box(p \land q) \rightarrow (\Box p \land \Box q)$ in modal system $K$

Published on 26 Mar 2026 - 13:00

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Deductively prove that $ \vdash (p \land q) \rightarrow p$

Published on 27 Mar 2026 - 5:39

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Constructing a Kripke model where $p \rightarrow \Box \Diamond q$ is false.

Published on 25 Mar 2026 - 4:18

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What is a logical constant, exactly?

Published on 09 Apr 2026 - 11:40

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If $P \iff Q$ is true, why does any proof of $Q$ have to use the fact that $P$ is true?

Published on 22 Jun 2023 - 6:11

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Questions about material implication and object language.

Published on 03 Apr 2026 - 12:30

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Why is "$P$ only if $Q$" equivalent to "if $P$ then $Q$"?

Published on 06 Apr 2026 - 22:45

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Business rules to propositional logic and truth tables

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How to form a CNF of following formula

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Is $\forall xP(x) \vee \neg \forall yP(y)$ a tautology in FOL?

Published on 12 Apr 2026 - 0:50

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Question about derivation of $\phi, \neg \phi \vdash \psi$ with constructive propositional logic system

Published on 02 Jul 2023 - 23:47

List Question

Determine the propositional form and truth value of the following

Explain why, if $P$ is equivalent to $Q$, then $\sim P$ is equivalent to $\sim Q$?

The principle of structural induction in logic

If we have proved that $n$ cannot be greater than $9$, have we also proved that the most it can be is $9$?

Proving $\Box(p \land q) \rightarrow (\Box p \land \Box q)$ in modal system $K$

Deductively prove that $ \vdash (p \land q) \rightarrow p$

Constructing a Kripke model where $p \rightarrow \Box \Diamond q$ is false.

What is a logical constant, exactly?

If $P \iff Q$ is true, why does any proof of $Q$ have to use the fact that $P$ is true?

Questions about material implication and object language.

Why is "$P$ only if $Q$" equivalent to "if $P$ then $Q$"?

Business rules to propositional logic and truth tables

How to form a CNF of following formula

Is $\forall xP(x) \vee \neg \forall yP(y)$ a tautology in FOL?

Question about derivation of $\phi, \neg \phi \vdash \psi$ with constructive propositional logic system

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