Boolean algebra

English

Etymology

Named after Template:W (1815–1864), an English mathematician, educator, philosopher and logician.

Noun

1. Template:Lb An algebraic structure $(\mathrm{\Sigma },\vee ,\wedge ,\sim ,0,1)$ where $\vee$ and $\wedge$ are idempotent binary operators, $\sim$ is a unary involutory operator (called "complement"), and 0 and 1 are nullary operators (i.e., constants), such that $(\mathrm{\Sigma },\vee ,0)$ is a commutative monoid, $(\mathrm{\Sigma },\wedge ,1)$ is a commutative monoid, $\wedge$ and $\vee$ distribute with respect to each other, and such that combining two complementary elements through one binary operator yields the identity of the other binary operator. (See Template:W.)

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2. Template:Lb Specifically, an algebra in which all elements can take only one of two values (typically 0 and 1, or "true" and "false") and are subject to operations based on AND, OR and NOT
3. Template:Lb The study of such algebras; Boolean logic, classical logic.

Synonyms

• Template:Sense switching algebra

Hypernyms

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  • De Morgan algebra
    • Ockham algebra
      • distributive lattice
• Template:L
  • residuated lattice
• MV-algebra

Hyponyms

• Template:L

Derived terms

• free Boolean algebra

Translations

• Chinese:

  Mandarin: Template:T+

• Czech: Template:T, Template:T
• French: Template:T+, Template:T
• German: Template:T
• Hungarian: Template:T+
• Italian: Template:T, Template:T, Template:T+
• Japanese: Template:T
• Korean: Template:T, Template:T
• Macedonian: Template:T
• Romanian: Template:T
• Russian: Template:T
• Serbo-Croatian: Template:T
• Swedish: Template:T

See also

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