Define the validity of a well-formed formula (wff)?

GATE 1988 · Discrete Mathematics · Propositional Logic · medium

Answer: A well-formed formula F is valid (a tautology) if and only if it is True under every interpretation, i.e. the last column of its truth table is all True.

1. Fix the meaning of an interpretation: An interpretation I assigns a truth value to every propositional variable that appears in F. With n variables there are 2^n distinct interpretations.
2. State the validity condition: F is valid (a tautology) precisely when value(F, I) = True for every interpretation I. Equivalently, the final column of the truth table of F contains only True.