Tautology (logic)

In propositional logic, a tautology (from the Greek word ταυτολογία) is a propositional formula that is always true, and is sometimes denoted by the symbol formula_1 (a symbol also reserved for the truth value 'true'). In other words, a tautology cannot be wrong. For example, formulae in maths are tautological, because they always hold true for any values. The philosopher Ludwig Wittgenstein first applied the term to propositional logic in 1921.
A statement in logic is considered contingent if it is neither a tautology nor false.
Some examples of tautologies in natural language include: 
These tautologies are sentences of the following form:
Indeed, if A is not true, then A is not true, so the tautology is still true.