A boolean domain B{\displaystyle \mathbb {B} } is a generic 2-element set, say, B={0,1}{\displaystyle \mathbb {B} =\{0,1\}}, whose elements are interpreted as logical values, typically, 0=false{\displaystyle 0=\mathrm {false} } and 1=true{\displaystyle 1=\mathrm {true} }.
A boolean variable x{\displaystyle x} is a variable that takes its value from a boolean domain, as x∈B{\displaystyle x\in \mathbb {B} }.