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In mathematics and mathematical logic, Boolean algebra is a branch of algebra.It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers.
In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties of both set operations and logic operations. A Boolean algebra can be seen as a generalization of a power set algebra or a field of sets, or its elements can be viewed as generalized ...
Boolean algebra (structure), a set with operations resembling logical ones; Boolean circuit, a mathematical model for digital logical circuits. Boolean data type is a data type, having two values (usually denoted true and false) Boolean expression, an expression in a programming language that produces a Boolean value when evaluated
Boolean algebra is a mathematically rich branch of abstract algebra. Stanford Encyclopaedia of Philosophy defines Boolean algebra as 'the algebra of two-valued logic with only sentential connectives, or equivalently of algebras of sets under union and complementation.' [1] Just as group theory deals with groups, and linear algebra with vector spaces, Boolean algebras are models of the ...
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.
In computer science, the Boolean (sometimes shortened to Bool) is a data type that has one of two possible values (usually denoted true and false) which is intended to represent the two truth values of logic and Boolean algebra. It is named after George Boole, who first defined an algebraic system of logic in the mid 19th century.
This is a list of topics around Boolean algebra and propositional logic. Articles with a wide scope and introductions. Algebra of sets; Boolean algebra (structure)
The algebraic structure that naturally builds on a Boolean domain is the Boolean algebra with two elements. The initial object in the category of bounded lattices is a Boolean domain. In computer science, a Boolean variable is a variable that takes values in some Boolean domain.