Question

show that $p \leftrightarrow q$ and $(p \land q) \lor (\neg p \land \neg q)$ are logically equivalent.

Answer 1

We have

$p\leftrightarrow q$ holds if and only if $p=q$ .

(p∧q)∨(¬p∧¬q) holds if and only if p∧q (which is p=1,q=1) holds or ¬p∧¬q (which is p=0, q=0) holds. This means $p=q$ (and is either 0 or 1).

The equivalence is proved.