Logical equivalence and the laws of logic begin with the idea that two compound statements may look different but behave exactly the same in every truth-value assignment. Having learned basic connectives and truth tables, we now use final truth-table columns to decide when two symbolic forms have the same meaning. Equivalent forms of compound statements are important because they allow implications, biconditionals, and exclusive-or statements to be rewritten using simpler connectives. In this lesson, equivalent forms of compound statements will be used to replace one logical expression by another without changing its truth value.

Let $s_1$ and $s_2$ be two statements. Then $s_1$ and $s_2$ are said to be \textbf{logically equivalent} if they have the same truth value for every assignment of truth values to their primitive statements. We write $s_1\Leftrightarrow s_2$.