noun

# Boolean algebra

Boolean algebra

**MLA Style**

"Boolean algebra." YourDictionary, n.d. Web. 06 December 2018. <https://www.yourdictionary.com/boolean-algebra>.

**APA Style**

Boolean algebra. (n.d.). Retrieved December 06th, 2018, from https://www.yourdictionary.com/boolean-algebra

**Boolean operators**AND, OR, and NOT. For example, “a + b” means “a OR b”, and its value is true as long as either a is true or b is true (or both). Boolean logic can be used to solve logical problems, and provides the mathematical tools fundamental to the design of digital computers. It is named after the mathematician George Boole. Also called

*Boolean logic*

See also logic gate

**MLA Style**

"Boolean algebra." YourDictionary, n.d. Web. 06 December 2018. <https://www.yourdictionary.com/boolean-algebra>.

**APA Style**

Boolean algebra. (n.d.). Retrieved December 06th, 2018, from https://www.yourdictionary.com/boolean-algebra

(*uncountable*)

- (algebra) A De Morgan algebra which also satisfies the law of excluded middle and the law of noncontradiction.
*The set of divisors of 30, with binary operators: g.c.d. and l.c.m., unary operator: division into 30, and identity elements: 1 and 30, forms a Boolean algebra.*-
*The nodes N*_{i}of a Boolean lattice can be labeled with Boolean formulae F(N_{i}), such that if node C is the meet of nodes A and B, then F(C) = F(A)F(B); if node C is the join of nodes A and B, then F(C) = F(A)+F(B); if node C is the complement of node A, then F(C) = F(A)'; and the 'â‰¤' order relation corresponds to logical entailment. A set of 'n' Boolean formulae could be called a "basis" for a 2^{n}-element Boolean algebra iff they are all mutually disjoint (i.e., the product of any pair is 0) and their Î£ (collective sum) is equal to 1. A set S of formulae could then generate a Boolean algebra inductively as follows: (base step) let P_{0}= S âˆª {(Î£S)'}, (inductive step) if a pair of formulae F and G in P_{i}are non-disjoint (i.e., FGâ‰ 0), then let P_{i+1}= (P_{i}âˆª {FG, F'G, FG'}) \ {F, G}, otherwise P_{i}is a basis. If CARD(P_{i})=n then the Boolean algebra will have 2^{n}elements which are all "linear combinations" of the basis elements, with a coefficient of either 0 or 1 for each term of each linear combination.

- (algebra, logic, computing) Specifically, an algebra in which all elements can take only one of two values (typically 0 and 1, or "true" and "false") and are subject to operations based on AND, OR and NOT
- (mathematics) The study of such algebras; Boolean logic, classical logic.

**MLA Style**

"Boolean algebra." YourDictionary, n.d. Web. 06 December 2018. <https://www.yourdictionary.com/boolean-algebra>.

**APA Style**

Boolean algebra. (n.d.). Retrieved December 06th, 2018, from https://www.yourdictionary.com/boolean-algebra

## boolean algebra - Computer Definition

See Boolean logic.

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**APA Style**