# Tautology

A formula of the language of propositional calculus taking the truth value "true" independently of the truth values "true" or "false" taken by its propositional variables. Examples: $A\supset A$, $A\lor\neg A$, $(A\supset B)\supset(\neg B\supset\neg A)$.

In general one can check whether a given propositional formula is a tautology by simply examining its truth table: the finite set of all combinations of values of its propositional variables. It is usual to give a presentation of propositional calculus which is both sound: every theorem deducible in the system is a tautology; and complete: every tautology is a theorem.