# 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.

### B

## Pages in category "Definitions/Boolean Algebras"

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

### B

- Definition:Boolean Algebra
- Definition:Boolean Algebra/Also defined as
- Definition:Boolean Algebra/Also known as
- Definition:Boolean Algebra/Axioms/Definition 1
- Definition:Boolean Algebra/Axioms/Definition 2
- Definition:Boolean Algebra/Definition 1
- Definition:Boolean Algebra/Definition 2
- Definition:Boolean Algebra/Definition 3