# Tautology

A propositional formula $P$ is a **tautology** (or valid) if $[P]=T$ for **all** Boolean Valuations.

Ex: $p∨¬p$ is a tautology.

What is the relationship between Tautology and Tautology and Semantics? Well, the semantics are not the rules themselves, but rather you can think of it like the grammar of Logic.

So when a formula $Q$ is a tautology, we write: $⊨Q$

The opposite of a Tautology is a Tautology is a Contradiction. Something that is neither a tautology nor a contradiction is a Tautology is a Contradiction. Something that is neither a tautology nor a contradiction is a Contradiction. Something that is neither a tautology nor a contradiction is a Contingent Formula.