Definition:Boolean Domain

Definition
A boolean domain $\Bbb B$ is a generic $2$-element set, say, $\Bbb B = \left\{{0, 1}\right\}$.

The elements are frequently interpreted as logical truth values, typically, $0 = \operatorname{False}$ and $1 = \operatorname{True}$.

In the study of pure Boolean algebra, it does not matter exactly how the elements of $\Bbb B$ are interpreted, or even what they are.

However, $\left\{{0, 1}\right\}$ and $\left\{{\operatorname{True}, \operatorname{False}}\right\}$ are sufficiently widely used as to be "standard" in all but name.

Linguistic Note
The word boolean has entered the field of computer science as a noun meaning a variable which can take one of (exactly) two values.

Note that although the modern usage renders it without a capital B, you will find that older texts use Boolean.