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Boolean functions are the subject of Boolean algebra and switching theory. [5] A Boolean function takes the form : {,} {,}, where {,} is known as the Boolean domain and is a non-negative integer called the arity of the function.
Boolean algebra also deals with functions which have their values in the set {0,1}. A sequence of bits is a commonly used example of such a function. Another common example is the totality of subsets of a set E: to a subset F of E, one can define the indicator function that takes the value 1 on F, and 0 outside F.
In computer science, a Boolean expression is an expression used in programming languages that produces a Boolean value when evaluated. A Boolean value is either true or false.A Boolean expression may be composed of a combination of the Boolean constants True/Yes or False/No, Boolean-typed variables, Boolean-valued operators, and Boolean-valued functions.
A Boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f : X → B, where X is an arbitrary set and where B is a Boolean domain, i.e. a generic two-element set, (for example B = {0, 1}), whose elements are interpreted as logical values, for example, 0 = false and 1 = true, i.e., a single bit of information.
Boolean domain, a set consisting of exactly two elements whose interpretations include false and true; Boolean circuit, a mathematical model for digital logical circuits. Boolean expression, an expression in a programming language that produces a Boolean value when evaluated; Boolean function, a function that determines Boolean values or operators
Boolean operation or Boolean operator may refer to: Boolean function, a function whose arguments and result assume values from a two-element set Boolean operation (Boolean algebra), a logical operation in Boolean algebra (AND, OR and NOT) Boolean operator (computer programming), part of a Boolean expression in a computer programming language
In contrast, converting between Booleans and integers (or any other types) still required explicit tests or function calls, as in ALGOL 60. This approach (Boolean is an enumerated type) was adopted by most later languages which had enumerated types, such as Modula, Ada, and Haskell.
In Boolean functions, each separate occurrence of a variable, either in inverse or uncomplemented form, is a literal. For example, if A {\displaystyle A} , B {\displaystyle B} and C {\displaystyle C} are variables then the expression A ¯ B C {\displaystyle {\bar {A}}BC} contains three literals and the expression A ¯ C + B ¯ C ...