Complement of Complement (Boolean Algebras)
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Theorem
Let $\struct {S, \vee, \wedge, \neg}$ be a Boolean algebra.
Then for all $a \in S$:
- $\map \neg {\neg a} = a$
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 $2$