Two statements are logically equivalent if they have identical truth values in all cases. Key equivalences: p => q ≡ ~p OR q (material implication). p => q ≡ ~q => ~p (contrapositive). p <=> q ≡ (p => q) AND (q => p). ~(~p) ≡ p (double negation). p AND (q OR r) ≡ (p AND q) OR (p AND r) (distribution). p OR (q AND r) ≡ (p OR q) AND (p OR r) (distribution). p OR (p AND q) ≡ p (absorption). p AND (p OR q) ≡ p (absorption). These equivalences allow simplification of complex compound statements without truth tables. They mirror set operation identities (AND <-> intersection, OR <-> union, NOT <-> complement).