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Implication

Prove: ∼ p⇒...

Question

Prove: $\sim (p \Rightarrow q) \equiv p \land (\sim q)$ .

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Solution

$p$ $q$ $\sim q$ $p ⟹ q$ $\sim (p ⟹ q)$ $p \land (\sim q)$
$T$ $T$ $F$ $T$ $F$ $F$
$T$ $F$ $T$ $F$ $T$ $T$
$F$ $T$ $F$ $T$ $F$ $F$
$F$ $F$ $T$ $T$ $F$ $F$
So, from the truth table , $\sim (p ⟹ q) \equiv p \land (\sim q) .$

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