Definition:Boolean Domain

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

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 $$\mathbb{B}$$ 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 two values".

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