In logic, a statement that cannot be denied without inconsistency. Thus, “All bachelors are either male or not male” is held to assert, with regard to anything whatsoever that is a bachelor, that it is male or it is not male. In the propositional calculus, even complicated symbolic expressions such as [(A ⊃ B) ∧ (C ⊃ ¬ B)] ⊃ (C ⊃ ¬ A) can be shown to be tautologies by displaying in a truth table every possible combination of T (true) and F (false) of its arguments A, B, C. A tautology can be purely formal (a statement form rather than a statement), and in some usages only such formal truths are tautologies.

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