1. The problem is to verify the logical equivalence: $\neg(p \lor q) \leftrightarrow (\neg p \land \neg q)$. 2. This is a classic example of De Morgan's Law in propositional logic, which states that the negation of a disjunction is equivalent to the conjunction of the negations. 3. The formula used is: $$\neg(p \lor q) = \neg p \land \neg q$$ 4. To understand why, consider the truth values: - $p \lor q$ is true if at least one of $p$ or $q$ is true. - Negating $p \lor q$ means it is false that $p$ or $q$ is true, so both must be false. - Hence, $\neg p$ and $\neg q$ must both be true, which is $\neg p \land \neg q$. 5. Therefore, the equivalence $\neg(p \lor q) \leftrightarrow (\neg p \land \neg q)$ holds true by De Morgan's Law. 6. This equivalence is fundamental in logic and helps simplify expressions involving negations and disjunctions.