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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/False or Yes/No, Boolean-typed variables, Boolean-valued operators, and Boolean-valued functions.
A law of Boolean algebra is an identity such as x ∨ (y ∨ z) = (x ∨ y) ∨ z between two Boolean terms, where a Boolean term is defined as an expression built up from variables and the constants 0 and 1 using the operations ∧, ∨, and ¬. The concept can be extended to terms involving other Boolean operations such as ⊕, →, and ≡ ...
In programming languages with a built-in Boolean data type, such as Pascal, C, Python or Java, the comparison operators such as > and ≠ are usually defined to return a Boolean value. Conditional and iterative commands may be defined to test Boolean-valued expressions.
Boolean operator (computer programming), part of a Boolean expression in a computer programming language; An operation or operator as characterized in the logical truth table; Logical operator, in logic, a logical constant used to connect two or more formulas; Set operation (Boolean), a set-theoretic operation in the algebra of sets (union ...
Boolean function, a function that determines Boolean values or operators; Boolean model (probability theory), a model in stochastic geometry; Boolean network, a certain network consisting of a set of Boolean variables whose state is determined by other variables in the network; Boolean processor, a 1-bit variable computing unit; Boolean ring, a ...
Venn diagram of . Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional.
A Boolean algebra is a set A, equipped with two binary operations ∧ (called "meet" or "and"), ∨ (called "join" or "or"), a unary operation ¬ (called "complement" or "not") and two elements 0 and 1 in A (called "bottom" and "top", or "least" and "greatest" element, also denoted by the symbols ⊥ and ⊤, respectively), such that for all elements a, b and c of A, the following axioms hold: [2]
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). [1] [2] Alternative names are switching function, used especially in older computer science literature, [3] [4] and truth function (or logical function), used in logic.