boolean

(definition)

Definition: (1) In computer science, entities having just two values: 1 or 0, true or false, on or off, etc. along with the operations and, or, and not. (2) In mathematics, entities from an algebra equivalent to intersection, union, and complement over subsets of a given set.

See also boolean expression, boolean function.

Note: A mathematical boolean algebra based on a set of size n has 2ⁿ values. The operations, intersection and union (or and and or), are commutative and associative, and each distributes over the other. Each operation has an identity, and complement produces the inverse. Binary logic is the boolean algebra which two values.

Author: PEB

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Entry modified 23 March 2009.
HTML page formatted Mon Feb 2 13:10:39 2015.

Cite this as:
Paul E. Black, "boolean", in Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 23 March 2009. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/boolean.html