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.