De Morgan's Laws (Boolean Algebras)

Theorem
Let $\left({S, \vee, \wedge, \neg}\right)$ be a Boolean algebra.

Then for all $a, b \in S$:


 * $\neg \left({a \vee b}\right) = \neg a \wedge \neg b$
 * $\neg \left({a \wedge b}\right) = \neg a \vee \neg b$

Also see

 * De Morgan's Laws (Logic)