(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

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 23 March 2009.

HTML page formatted Fri Feb 23 10:06:07 2018.

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: https://www.nist.gov/dads/HTML/boolean.html