# 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 $\struct {S, \vee, \wedge, \neg}$, where $\vee$ and $\wedge$ are binary, and $\neg$ is a unary operation.

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

 $(\text {BA}_1 0)$ $:$ $S$ is closed under $\vee$, $\wedge$ and $\neg$ $(\text {BA}_1 1)$ $:$ Both $\vee$ and $\wedge$ are commutative $(\text {BA}_1 2)$ $:$ Both $\vee$ and $\wedge$ distribute over the other $(\text {BA}_1 3)$ $:$ Both $\vee$ and $\wedge$ have identities $\bot$ and $\top$ respectively $(\text {BA}_1 4)$ $:$ $\forall a \in S: a \vee \neg a = \top, a \wedge \neg a = \bot$

## Source of Name

This entry was named for George Boole.

## Subcategories

This category has only the following subcategory.

## Pages in category "Definitions/Boolean Algebras"

The following 11 pages are in this category, out of 11 total.