Chapter 1.3, Problem 21E

Each of Exercises 20-32 asks you to show that two compound propositions are logically equivalent. To do this, either show that both sides are true, or that both sides are false, for exactly the same combinations of truth values of the propositional variables in these expressions (whichever is easier).

21. Show that $\neg \left(p\leftrightarrow q\right)$and $p\leftrightarrow \neg q$are logically equivalent.