(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 2 ^{n} 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 Wed Mar 13 12:42:45 2019.

Cite this as:

Paul E. Black, "boolean", in
*Dictionary of Algorithms and Data Structures* [online], Paul E. Black, ed. 23 March 2009. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/boolean.html