# Boolean expression

In computer science, a **Boolean expression** is used expression in a programming language that produces a Boolean value when evaluated, that is one of **true** or **false**. A Boolean expression may be composed of a combination of the Boolean constants **true** or **false**, Boolean-typed variables, Boolean-valued operators, and Boolean-valued functions.[1]

Boolean expressions correspond to propositional formulas in logic and are a special case of Boolean circuits.[2]

## Boolean operators

Most programming languages have the Boolean operators OR, AND and *NOT*; in C and some newer languages, these are represented by "||" (double pipe character), "&&" (double ampersand) and "!" (exclamation point) respectively, while the corresponding bitwise operations are represented by "|", "&" and "~" (tilde).[3] In the mathematical literature the symbols used are often "+" (plus), "**·**" (dot) and overbar, or "∨" (cup), "∧" (cap) and "¬" or "′" (prime).

## Examples

- The expression "5 > 3" is evaluated as
**true**. - The expression "3 > 5" is evaluated as
**false**. - "5>=3" and "3<=5" are equivalent Boolean expressions, both of which are evaluated as
**true**. - "typeof true" returns "boolean" and "typeof false" returns "boolean"
- Of course, most Boolean expressions will contain at least one variable (X > 3), and often more (X > Y).

## References

- Gries, David; Schneider, Fred B. (1993), "Chapter 2. Boolean Expressions",
*A Logical Approach to Discrete Math*, Monographs in Computer Science, Springer, p. 25ff, ISBN 9780387941158. - van Melkebeek, Dieter (2000),
*Randomness and Completeness in Computational Complexity*, Lecture Notes in Computer Science,**1950**, Springer, p. 22, ISBN 9783540414926. - E.g. for Java see Brogden, William B.; Green, Marcus (2003),
*Java 2 Programmer*, Que Publishing, p. 45, ISBN 9780789728616.

## External links

- The Calculus of Logic, by George Boole, Cambridge and Dublin Mathematical Journal Vol. III (1848), pp. 183–98.