English-Bulgarian translations for boolean algebra
Definition of boolean algebra
- An algebraic structure where and are idempotent binary operators, is a unary involutory operator , and 0 and 1 are nullary operators , such that is a commutative monoid, is a commutative monoid, and distribute with respect to each other, the identity of each monoid acts as the zero of the other monoid, and such that combining two complementary elements through one binary operator yields the identity of the other binary operator. #Axiomatics}}
- Specifically, an algebra in which all elements can take only one of two values and are subject to operations based on AND, OR and NOT may need to be split into: "an algebra of logical values" and "an algebra of ''two'logical values" --
Examples
- 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.
- A Boolean algebra is a De Morgan algebra which also satisfies the law of excluded middle and the law of noncontradiction.
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