Same truth table, same meaning

Two statements are equivalent, written $\equiv$, when they have the same truth value in every row.

De Morgan’s laws: $\lnot (P \land Q) \equiv \lnot P \lor \lnot Q$, and $\lnot (P \lor Q) \equiv \lnot P \land \lnot Q$.

Implication can be rewritten: $P \Rightarrow Q \equiv \lnot P \lor Q$.