Boolean algebra

English Etymology Named after George Boole (1815–1864), an English mathematician, educator, philosopher and logician. Noun en algebra An algebraic structure where and are idempotent binary operators, is a unary involutory operator (called "complement"), and 0 and 1 are nullary operators (i.e., constants), such that is a commutative monoid, is a commutative monoid, and 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 Boolean algebra (structure)#Axiomatics.) en The set of divisors of 30, with binary operators: g.c.d. and l.c.m., unary operator: division into 30, and identity elements: 1 and 30, forms a Boolean algebra. en A Boolean algebra is a De Morgan algebra which also satisfies the law of excluded middle and the law of noncontradiction. en algebra logic computing 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 en mathematics The study of such algebras; Boolean logic, classical logic. Synonyms Specifically ... switching algebra Hypernyms en Kleene algebra De Morgan algebra Ockham algebra distributive lattice en Heyting algebra residuated lattice MV-algebra Hyponyms en complete Boolean algebra Derived terms free Boolean algebra Translations algebraic structure Bulgarian: bg Булева алгебра f Chinese: Mandarin: cmn 布爾代數 Bù'ěr dàishù Czech: cs Booleova algebra f, cs booleovská algebra f French: fr algèbre de Boole f, fr algèbre booléenne f German: de boolesche Algebra f Hungarian: hu Boole-algebra Italian: it algebra booleana f, it reticolo booleano m, it algebra di Boole f Japanese: ja ブール代数 Būru-daisū Korean: ko ^불 대수, ko ^부울 대수 Macedonian: mk Булова алге́бра f Polish: pl algebra Boole'a f Romanian: ro algebră booleană f Russian: ru бу́лева а́лгебра f Serbo-Croatian: sh Booleova algebra f Swedish: sv Boolesk algebra See also en Boolean lattice en Boolean ring en eponyms