Axiom:Boolean Algebra/Axioms/Formulation 1

Axiom

A Boolean algebra is an algebraic system $\struct {S, \vee, \wedge, \neg}$, where $\vee$ and $\wedge$ are binary, and $\neg$ is a unary operation.

Furthermore, these operations are required to satisfy the following axioms:

$(\text {BA}_1 0)$	$:$	$S$ is closed under $\vee$, $\wedge$ and $\neg$
$(\text {BA}_1 1)$	$:$	Both $\vee$ and $\wedge$ are commutative
$(\text {BA}_1 2)$	$:$	Both $\vee$ and $\wedge$ distribute over the other
$(\text {BA}_1 3)$	$:$	Both $\vee$ and $\wedge$ have identities $\bot$ and $\top$ respectively
$(\text {BA}_1 4)$	$:$	$\forall a \in S: a \vee \neg a = \top, a \wedge \neg a = \bot$