A statement which is neither a tautology nor a contradiction is called contingency . ( ) Any two compound statements A and B are said to be logically equivalent or simply equivalent if the columns corresponding to A and B in the truth table have identical truth values . The logical equivalence of the statements A and B is denoted by A B ≡ or A B ⇔ . Further note that if A and B are logically equivalent, then A B ↔ must be a tautology .
( ) Some laws of equivalence: Idempotent Laws: (i) p ≡ (ii) p ≡ Commutative Laws: (i) p ≡ (ii) p ≡ Associative Laws: (i) p ) ≡ ) ∨ (ii) p ) ≡ ) ∧ . Distributive Laws: (i) p ≡ (ii) p ≡ Identity Laws: