# 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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### Prove that the intersection of definable sets is definable

Hello I have a question : $F$ is a family of definable sets. Prove that the intersection of all the sets in the family is definable. ($F$ could be infinite) Definition (Definable): a set $K$ of ...
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### Find indefinable set that is included in definable set.

Find $K\subseteq \operatorname{Ass}$ and $K'\subseteq K$ such that $K$ is definable but $K'$ is not. Definition (Definable): a set $K$ of assignments is definable if there is a set of formulas A ...
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### I'm wodering if this statement is provable in logic $\lnot \alpha \to \lnot \lnot \lnot \alpha )$

I've encountered this statement in my final exam $$\lnot \alpha \to \lnot \lnot \lnot \alpha )$$ there was no open parenthesis and from what I know this is invalid (not a well-formed formula) so ...
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### Why is a statement “vacuously true” if the hypothesis is false, or not satisfied?

Why isn't a conditional statement said to "not apply" instead of be "vacuously true" if the hypothesis is not satisfied? That would seem more appropriate.
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### Exam preparation: logic - problems on (maximally) consistent sets

I am preparing for an exam on aspects of Logic related to propositional and first order logic. One of my revision exam questions is . I have attempted this question but I am really struggling with ...
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