Boolean algebra
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(algebra) An algebraic structure (ðŽ,âš,â§,âŒ,0,1) where âš and ⧠are idempotent binary operators, ⌠is a unary involutory operator (called complement
), and 0 and 1 are nullary operators (i.e., constants), such that (ðŽ,âš,0) is a commutative monoid, (ðŽ,â§,1) is a commutative monoid, ⧠and âš distribute with respect to each other, and such that combining two complementary elements through one binary operator yields the identity of the other binary operator. (See Boolean algebra (structure)#Axiomatics.)
Boolean algebra
In the seminar, we demonstrated that a Boolean algebra is an algebraic structure (Σ, âš, â§, âŒ, 0, 1) in which the binary operations âš and ⧠are idempotent, the unary operator ⌠is an involution called complement, 0 and 1 are constants, (Σ, âš, 0) and (Σ, â§, 1) form commutative monoids, âš and ⧠distribute over each other, and combining two complementary elements with one binary operation yields the identity of the other.
In the seminar, we demonstrated that a Boolean algebra is an algebraic structure (Σ, âš, â§, âŒ, 0, 1) in which the binary operations âš and ⧠are idempotent, the unary operator ⌠is an involution called complement, 0 and 1 are constants, (Σ, âš, 0) and (Σ, â§, 1) form commutative monoids, âš and ⧠distribute over each other, and combining two complementary elements with one binary operation yields the identity of the other.
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