Logical Equivalence

Two propositions are logically equivalent when they have the same truth value under every possible assignment of their simple propositions.

That makes equivalence stronger than “these happened to agree in one example.” To disprove equivalence, a single counterexample valuation is enough. To establish semantic equivalence by truth table, every row must match.

Examples worth understanding structurally include the contrapositive, De Morgan transformations, material implication, and double negation. When you are practicing a named rule, however, semantic equivalence alone is not enough: the transformation must match the rule actually cited.

Use the Equivalence lab to predict first, then reveal the complete pair of truth vectors and the first differing row when one exists.