Definition:Two (Boolean Algebra)

Definition
Denote with $\top$ the canonical tautology.

Denote with $\bot$ the canonical contradiction.

Define $\mathbf 2 := \left\{{\bot, \top}\right\}$, read two.

When endowed with the logical operations $\lor$, $\land$ and $\neg$, $\mathbf 2$ becomes a Boolean algebra.

This is shown on Two is Boolean Algebra.

Define $\preceq$ to be the poset determined by putting $\bot \preceq \top$.

When endowed with the logical operations $\lor$, $\land$ and $\neg$, $\mathbf 2$ becomes a Boolean lattice.

Also see

 * Two (Category), the category $\mathbf 2$ becomes when viewed as a poset category.