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An algebraic structure (Σ,∨,∧,∼,0,1) 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 (Σ,∨,0) is a commutative monoid, (Σ,∧,1) 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.)
Definition source: English Wiktionary via Wiktextract
Topics: algebra, mathematics, sciences
Examples
- 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.
- A Boolean algebra is a De Morgan algebra which also satisfies the law of excluded middle and the law of noncontradiction.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
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
Definition source: English Wiktionary via Wiktextract
Topics: algebra, computing, engineering, human-sciences, logic, mathematics, natural-sciences, philosophy, physical-sciences, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
The study of such algebras; Boolean logic, classical logic.
Definition source: English Wiktionary via Wiktextract
Topics: mathematics, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
a system of symbolic logic devised by George Boole; used in computers
Definition source: Princeton WordNet 3.0
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: Boolean logic
Antonyms: none provided
Broader terms: symbolic logic, mathematical logic, formal logic
Named after George Boole (1815–1864), an English mathematician, educator, philosopher and logician.
Across languages
Translations
20 source translations are retained for this English entry.
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Bulgarian:
Булева алгебра
— algebraic structure
-
Chinese Mandarin:
布爾代數 /布尔代数
(Bù'ěr dàishù)
— algebraic structure
-
Czech:
Booleova algebra
— algebraic structure
-
Czech:
booleovská algebra
— algebraic structure
-
French:
algèbre de Boole
— algebraic structure
-
French:
algèbre booléenne
— algebraic structure
-
German:
boolesche Algebra
— algebraic structure
-
Hungarian:
Boole-algebra
— algebraic structure
-
Italian:
algebra booleana
— algebraic structure
-
Italian:
reticolo booleano
— algebraic structure
-
Italian:
algebra di Boole
— algebraic structure
-
Japanese:
ブール代数
(Būru-daisū)
— algebraic structure
-
Korean:
불 대수
(Bul daesu)
— algebraic structure
-
Korean:
부울 대수
(Buul daesu)
— algebraic structure
-
Macedonian:
Булова алге́бра
(Bulova algébra)
— algebraic structure
-
Polish:
algebra Boole'a
— algebraic structure
-
Romanian:
algebră booleană
— algebraic structure
-
Russian:
бу́лева а́лгебра
(búleva álgebra)
— algebraic structure
-
Serbo-Croatian:
Booleova algebra
— algebraic structure
-
Swedish:
Boolesk algebra
— algebraic structure
