Let p, q be propositions. Using only the Truth Table, decide whether p does not imply p => q is True or False.

GATE 1994 · Discrete Mathematics · Propositional Logic · medium

Answer: True — p does not logically imply p => q

1. Build truth table for p and p => q: Row: p=T, q=T => p=>q=T. Row: p=T, q=F => p=>q=F. Row: p=F, q=T => p=>q=T. Row: p=F, q=F => p=>q=T.
2. Find the counterexample: Row p=T, q=F: p is True but p=>q is False. This is a valid counterexample.