(Proving a biconditional)
For propositions \(P\) and \(Q\), \(P\iff Q\) is equivalent to the conjunction of \(P \implies Q\) and \(\neg P \implies \neg Q\), since \(\neg P\implies\neg Q\) is the contrapositive of \(Q\implies P\).
(Proving a biconditional)
For propositions \(P\) and \(Q\), \(P\iff Q\) is equivalent to the conjunction of \(P \implies Q\) and \(\neg P \implies \neg Q\), since \(\neg P\implies\neg Q\) is the contrapositive of \(Q\implies P\).