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# Boolean algebra

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 operator: division into 30, and identity elements: 1 and 30, forms a Boolean algebra.

b) An algebra with two binary operators which are both associative, both commutative, such that both operators are distributive with respect to each other, with a pair of identity elements: one for each operator, and a unary complementation operator which simultaneously yields the inverse with respect to both operators.

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• 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

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• 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

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• 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