A Boolean domain $\mathbb{B}$ is a generic 2-element set, say, $\mathbb{B} = \{ 0, 1 \}$ whose elements are interpreted as logical values, typically, $0 = \mathrm{false}$ and $1 = \mathrm{true}$

A Boolean variable $x$ is a variable that takes its value from a Boolean domain, as $x \in \mathbb{B}$