In a Boolean ring, the multiplicative operation is idempotent, so every element equals its square.

In the seminar, we studied how Boolean rings arise in the algebraic formulation of classical logic.

During the lecture, the professor used a Hasse diagram to illustrate the structure of a Boolean lattice.

When debugging the program, I noticed that several Boolean variables were unintentionally shared between threads.

Professor Li assigned a homework problem asking us to classify all Boolean functions of three variables by their symmetry properties.

To optimize the circuit, the engineer minimized the Boolean function using Karnaugh maps.

Before running the algorithm, she set the Boolean variable to true to enable the debug mode.

Understanding Boolean logic is essential for designing reliable digital circuits.

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.

Several researchers studied the automorphisms of Boolean lattices arising from finite sets.