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...

In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties...

what Boolean algebras are to set theory and ordinary propositional logic. Interior algebras form a variety of modal algebras. An interior algebra is an...

mathematics, a complete Boolean algebra is a Boolean algebra in which every subset has a supremum (least upper bound). Complete Boolean algebras are used to construct...

a list of topics around Boolean algebra and propositional logic. Algebra of sets Boolean algebra (structure) Boolean algebra Field of sets Logical connective...

In mathematics, a Heyting algebra (also known as pseudo-Boolean algebra) is a bounded lattice (with join and meet operations written ∨ and ∧ and with...

Topological Boolean algebra may refer to: In abstract algebra and mathematical logic, topological Boolean algebra is one of the many names that have been...

Boolean algebra is a mathematically rich branch of abstract algebra. Stanford Encyclopaedia of Philosophy defines Boolean algebra as 'the algebra of two-valued...

In abstract algebra, a monadic Boolean algebra is an algebraic structure A with signature ⟨·, +, ', 0, 1, ∃⟩ of type ⟨2,2,1,0,0,1⟩, where ⟨A, ·, +, ',...

Look up Boolean algebra in Wiktionary, the free dictionary. Boolean algebra is the algebra of truth values and operations on them. Boolean algebra may also...

An example is the ring of integers modulo 2. Every Boolean ring gives rise to a Boolean algebra, with ring multiplication corresponding to conjunction...

and abstract algebra, the two-element Boolean algebra is the Boolean algebra whose underlying set (or universe or carrier) B is the Boolean domain. The...

free Boolean algebra is a Boolean algebra with a distinguished set of elements, called generators, such that: Each element of the Boolean algebra can be...

Any set of sets closed under the set-theoretic operations forms a Boolean algebra with the join operator being union, the meet operator being intersection...

In mathematics, the Boolean prime ideal theorem states that ideals in a Boolean algebra can be extended to prime ideals. A variation of this statement...

logical function), used in logic. Boolean functions are the subject of Boolean algebra and switching theory. A Boolean function takes the form f : { 0 ...

mathematical logic, minimal axioms for Boolean algebra are assumptions which are equivalent to the axioms of Boolean algebra (or propositional calculus), chosen...

play an essential role in the representation theory of Boolean algebras. Every Boolean algebra can be represented as a field of sets. A field of sets...

In mathematics, Stone's representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a certain field of sets. The theorem...

logic and Boolean algebra. It is named after George Boole, who first defined an algebraic system of logic in the mid 19th century. The Boolean data type...

from a two-element set Boolean operation (Boolean algebra), a logical operation in Boolean algebra (AND, OR and NOT) Boolean operator (computer programming)...

In Boolean algebra, the inclusion relation a ≤ b {\displaystyle a\leq b} is defined as a b ′ = 0 {\displaystyle ab'=0} and is the Boolean analogue to the...

all Robbins algebras are Boolean algebras. This was proved in 1996, so the term "Robbins algebra" is now simply a synonym for "Boolean algebra". In 1933...

In mathematics and abstract algebra, a relation algebra is a residuated Boolean algebra expanded with an involution called converse, a unary operation...

TRUE just when exactly one of its arguments is. Using the laws of Boolean algebra, every propositional logic formula can be transformed into an equivalent...

values (usually "true" and "false") Boolean algebra, a logical calculus of truth values or set membership Boolean algebra (structure), a set with operations...

the Boolean algebra of the power set of a finite set. For infinite Boolean algebras, this is no longer true, but every infinite Boolean algebra can be...

Boolean arithmetic; The primary algebra (Chapter 6 of LoF), whose models include the two-element Boolean algebra (hereinafter abbreviated 2), Boolean...

residuated Boolean algebra is a residuated lattice whose lattice structure is that of a Boolean algebra. Examples include Boolean algebras with the monoid...

the Information Age. Shannon was the first to describe the use of Boolean algebra that are essential to all digital electronic circuits, and was one...