# Boolean algebra

- A Boolean algebra is a system consisting of a set S and two operations, n and ? (cap and cup), subject to the following axioms. For all sets a,b,c, that are members of S:1 a n (b n c) = (a n b) n c.Also a ? (b ? c) = (a ? b) ? c (associativity)2 a n b = b n a.Also a ? b = b ? a (commutativity)3 a n (b ? c) = (a n b) ? (a n c).Also a ? (b n c) = (a ? b) n (a ? c) (distributivity)4 There belong to S two elements, 0 and 1, with the properties a ? 0 = a; a n 1 = a (identity)5 For each set a in S there exists a set a' with the properties that a ? a' = 1, a n a' = 0 (complementation).The propositional calculus can be represented as a Boolean algebra, with n representing &, ? representing ∨, and 1 = T, 0 = F. The Boolean operators are then the truth functors, such as &, ∨, and ¬. A Boolean search is a search for things meeting a condition defined with these operators.

*Philosophy dictionary.
Academic.
2011.*

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**Boolean algebra**— statusas T sritis automatika atitikmenys: angl. Boolean algebra vok. Boolesche Algebra, f rus. булева алгебра, f pranc. algèbre de Boole, f ryšiai: sinonimas – Bulio algebra … Automatikos terminų žodynas**Boolean algebra**— This article discusses the subject referred to as Boolean algebra. For the mathematical objects, see Boolean algebra (structure). Boolean algebra, as developed in 1854 by George Boole in his book An Investigation of the Laws of Thought,[1] is a… … Wikipedia**Boolean algebra**— /booh lee euhn/ 1. Logic. a deductive logical system, usually applied to classes, in which, under the operations of intersection and symmetric difference, classes are treated as algebraic quantities. 2. Math. a ring with a multiplicative identity … Universalium**Boolean Algebra**— A division of mathematics which deals with operations on logical values. Boolean algebra traces its origins to an 1854 book by mathematician George Boole. The distinguishing factor of Boolean algebra is that it deals only with the study of binary … Investment dictionary**Boolean algebra**— noun a system of symbolic logic devised by George Boole; used in computers • Syn: ↑Boolean logic • Hypernyms: ↑symbolic logic, ↑mathematical logic, ↑formal logic * * * noun Usage: usually capitalized B … Useful english dictionary**Boolean algebra**— noun a) 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 The set of divisors of 30, with binary operators: g.c.d. and l.c.m., unary… … Wiktionary**Boolean algebra**— noun Date: circa 1889 an algebraic system that consists of a set closed under two binary operations and that can be described by any of various systems of postulates all of which can be deduced from the postulates that each operation is… … New Collegiate Dictionary**Boolean algebra**— See comparative sociology ; qualitative comparative analysis … Dictionary of sociology**boolean algebra**— mathematical set with operations whose rules are any of various equivalent systems of postulates … English contemporary dictionary**Boolean algebra**— Bool′e•an al′gebra [[t]ˈbu li ən[/t]] n. pho a system of symbolic logic dealing with the relationship of sets: the basis of logic gates in computers • Etymology: 1885–90; after G. Boole (1815–64), English mathematician; see an I … From formal English to slang