Equivalent forms of compound statements allow us to replace one symbolic expression by another without changing truth values. Among the most frequently used equivalences are De Morgan's Laws. These laws explain how negation passes through conjunction and disjunction. In this lesson, De Morgan's Laws will be used to negate compound statements, simplify expressions, and translate English statements into logically accurate negations.

Let $p$ and $q$ be primitive statements. Then $$\begin{equation*} \neg(p\land q)\Leftrightarrow\neg p\lor\neg q \end{equation*}$$ and $$\begin{equation*} \neg(p\lor q)\Leftrightarrow\neg p\land\neg q. \end{equation*}$$ These are called \textbf{De Morgan's Laws}.