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
- Definitions/Boolean Lattices (5 P)
Pages in category "Definitions/Boolean Algebras"
The following 10 pages are in this category, out of 10 total.