The laws of logic often appear in pairs. When conjunction and disjunction are interchanged, and tautology and contradiction are interchanged, one valid law often produces another valid law. This symmetry is called duality. In this lesson, duality in logical equivalence will be used to form dual statements and understand why many laws of logic occur in matching pairs.

Let $s$ be a statement that contains no logical connectives other than $\land$ and $\lor$. The \textbf{dual} of $s$, denoted by $s^d$, is obtained by replacing each occurrence of $\land$ by $\lor$, each occurrence of $\lor$ by $\land$, each occurrence of $T_0$ by $F_0$, and each occurrence of $F_0$ by $T_0$.