Tautologies and contradictions

Definition 2.3.11   A proposition which is always true is called a tautology.

The column of a tautology in a truth table contains only T's. For example, if $p$ is a proposition, then $p \vee \Bar{p}$ is a tautology. We could have used tautologies for proving all the previous laws; just add an extra column to each truth table, corresponding to the specific logical equivalence and check that this columns contains only T's.

Definition 2.3.12   A proposition which is always false is called a contradiction.

The column of a contradiction in a truth table contains only F's. For example, if $p$ is a proposition, then $p \wedge \Bar{p}$ is a contradiction.