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Prove that

(a) The sentence $P ↔ Q$ has the same truth table as $(P → Q) ∧ (Q → P)$.

(b) The neg statement $\neg (\neg P)$ has the same truth table as $P$, and $\neg (\neg (\neg P))$ than $\neg P$.

(c) The sentence $P → Q$ has the same truth table as $\neg P ∨ Q$.

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1 Answers 1

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Why don't you try actually doing the truth tables? No offense but these are essentially trivial.

Here's a hint: the output values you want will be the truth assignments given to the last binary connective which acts upon the other parts - for example, in the first one, it will be the $\wedge$ connective.