In the seminar, we demonstrated that a Boolean algebra is an algebraic structure (Σ, ∨, ∧, ∼, 0, 1) in which the binary operations ∨ and ∧ are idempotent, the unary operator ∼ is an involution called complement, 0 and 1 are constants, (Σ, ∨, 0) and (Σ, ∧, 1) form commutative monoids, ∨ 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, ∨, ∧, ∼, 0, 1) in which the binary operations ∨ and ∧ are idempotent, the unary operator ∼ is an involution called complement, 0 and 1 are constants, (Σ, ∨, 0) and (Σ, ∧, 1) form commutative monoids, ∨ and ∧ distribute over each other, and combining two complementary elements with one binary operation yields the identity of the other.
ゼミでは、ブール代数が、二項演算 ∨ と ∧ が冪等で、単項演算 ∼ が補元と呼ばれる自己逆な演算であり、0 と 1 が定数で、(Σ, ∨, 0) と (Σ, ∧, 1) が可換モノイドをなすとともに、∨ と ∧ が互いに分配律を満たし、互いに補元である二つの元を一方の二項演算で結合すると他方の単位元になるような代数的構造であることを示しました。
