Complement of Complement (Boolean Algebras)

Theorem

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

Then for all $a \in S$:

$\neg (\neg a) = a$

Proof

Follows directly from Complement in Boolean Algebra is Unique.

$\blacksquare$

Sources

• 2008: Paul Halmos and Steven Givant: Introduction to Boolean Algebras ... (previous) ... (next): $\S 2$: Exercise $2$