p => q is logically equivalent to ~p OR q. Proof by truth table: when p=T,q=T both give T; p=T,q=F both give F; p=F,q=T both give T; p=F,q=F both give T. This equivalence is useful for recognizing tautologies and simplifying compound statements. The negation of p => q is p AND ~q (not another implication).