Complement of Complement (Boolean Algebras)

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 $2$
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.