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Boolean logic defines an abstract mathematical structure. By a Boolean algebra we mean a set B together with two binary operations +, ∙ on B (known as addition and multiplication respectively) and a unary operation ' on B (called complementary) satisfying the following axioms:
Boolean logic defines an abstract mathematical structure. By a Boolean algebra we mean a set B together with two binary operations +, ∙ on B (known as addition and multiplication respectively) and a unary operation ' on B (called complementary) satisfying the following axioms:
Axiom. 1. The operations are commutative; i.e.,
a + b = b .+ a, a ∙ b = b ∙ a for all a, b ϵ B
Axiom. 2. Each binary operation distributes over the other; i.e.,
a + (b ∙ c) = (a + b) ∙ (a + c)
and a ∙ (b + c) = (a ∙ b) + (a ∙ c) for all a, b, c ϵ B
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