Mathematical Logic Logical Equivalence Definition 12.20 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 . From the definition, it is clear that, if A and B are logically equivalent, then A ⇔ B must be tautology . Some Laws of Equivalence 1. Idempotent Laws (i) p ∨ p ≡ p (ii) p ∧ p ≡ p . Proof In the above truth table for both p , p ∨ p and p ∧ p have the same truth values. Hence p ∨ p ≡ p and ...