Distributive laws are part of a larger collection called the laws of logic. These laws allow compound statements to be rewritten step by step while preserving logical equivalence. They play the same role in logic that algebraic identities play in algebra. In this lesson, laws of logic will be organized and applied to simplify compound statements and justify each transformation.

Let $s_1$ and $s_2$ be two statements. Then $s_1$ and $s_2$ are logically equivalent if $s_1\leftrightarrow s_2$ is a tautology. Thus, $s_1\Leftrightarrow s_2$ means that $s_1$ and $s_2$ have the same truth value under every assignment of truth values to their primitive statements.