We want to know whether \(\neg(P \vee Q)\) is logically equivalent to \(\neg P \wedge \neg Q\text{.}\) Make a truth table which includes both statements:
| \(P\) | \(Q\) | \(\neg(P \vee Q)\) | \(\neg P \wedge \neg Q\) |
| T | T | F | F |
| T | F | F | F |
| F | T | F | F |
| F | F | T | T |
Since in every row the truth values for the two statements are equal, the two statements are logically equivalent.