Propositional form X is tautologous (i.e., X is a tautology) iff it is impossible for X to be false. In other words, X is necessarily true.
Example from everyday life: 'If x is taller than y and y is taller than z, then x is taller than z'
Example from categorical logic: 'All S are S'
Example from propositional logic: '[(p ﬤ q) ﬤ p] ﬤ p' (this is known as "Peirce's Law," after Charles Sanders Peirce [1839-1914])
Example from predicate logic: '(x)(Øx ﬤ Øx)'
