Two propositions are logically equivalent if they always have the same truth value. That is, the propositions p and q are logically equivalent if p is true whenever q is true and p is false whenever q is false. The proposition (p ↔ q) is always true if and only if p and q are logically equivalent. For example, p is logically equivalent to p, to (p & p), and to (p | p); (p | (!p)) is logically equivalent to TRUE; (p & !p) is logically equivalent to FALSE; (p ↔ p) is logically equivalent to TRUE; and (p → q) is logically equivalent to (!p | q).