Method of Truth Tables/Proof of Tautology

Proof Technique
This is used to establish whether or not a given propositional formula is a tautology for boolean interpretations; that, is valid in all boolean interpretations.

Let $P$ be a propositional formula we wish to validate.

Subsequently, determine its truth table.

In the column under the main connective of $P$ itself can be found the truth value of $P$ for each boolean interpretation.


 * If this contains nothing but $\T$, then $P$ is a tautology.
 * If this contains nothing but $\F$, then $P$ is a contradiction.
 * If this contains $\T$ for some boolean interpretations and $\F$ for others, then $P$ is a contingent statement.