Category:Definitions/Boolean Algebras

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This category contains definitions related to Boolean Algebras.
Related results can be found in Category:Boolean Algebras.

A Boolean algebra is an algebraic system $\left({S, \vee, \wedge, \neg}\right)$, where $\vee$ and $\wedge$ are binary, and $\neg$ is a unary operation.

Furthermore, these operations are required to satisfy the following axioms:

\((BA_1 \ 0)\)   $:$   $S$ is closed under $\vee$, $\wedge$ and $\neg$             
\((BA_1 \ 1)\)   $:$   Both $\vee$ and $\wedge$ are commutative             
\((BA_1 \ 2)\)   $:$   Both $\vee$ and $\wedge$ distribute over the other             
\((BA_1 \ 3)\)   $:$   Both $\vee$ and $\wedge$ have identities $\bot$ and $\top$ respectively             
\((BA_1 \ 4)\)   $:$   $\forall a \in S: a \vee \neg a = \top, a \wedge \neg a = \bot$