Two-element Boolean algebra

Example

The two-element Boolean algebra is the set $\{0, 1\}$ with these operations. $a \wedge b = 1$ if and only if $a = b = 1$. $a \vee b = 0$ if and only if $a = b = 0$. $\neg 0 = 1$ and $\neg 1 = 0$. It satisfies the axioms of a Boolean algebra, with $0$ as least element and $1$ as greatest element.

Remarks

If $1$ means true and $0$ means false, then $\wedge$, $\vee$ and $\neg$ are the connectives and, or and not. An equation in the Boolean operations holds in all Boolean algebras if and only if it holds in the two-element Boolean algebra. It is isomorphic to the power set of a set with one element.

Explanations

L1 human

The two-element Boolean algebra is the algebra of true and false. It is also the algebra of one bit in a digital circuit.