Non-Equivalence as Conjunction of Disjunction with Disjunction of Negations/Proof by Truth Table

Proof
We apply the Method of Truth Tables.

As can be seen by inspection, the truth values under the main connectives match for all boolean interpretations.

$\begin{array}{|cccc||ccccccccc|} \hline \neg & (p & \iff & q) & (p & \lor & q) & \land & (\neg & p & \lor & \neg & q) \\ \hline \F & \F & \T & \F & \F & \F & \F & \F & \T & \F & \T & \T & \F \\ \T & \F & \F & \T & \F & \T & \T & \T & \T & \F & \T & \F & \T \\ \T & \T & \F & \F & \T & \T & \F & \T & \F & \T & \T & \T & \F \\ \F & \T & \T & \T & \T & \T & \T & \F & \F & \T & \F & \F & \T \\ \hline \end{array}$