Axioms of Boolean Algebra

Associativity

$a \lor (b \lor c) = a \lor (b \lor c)$

$a \wedge (b \wedge c) = a \wedge (b \wedge c)$

Commutativity

$a \lor b = b \lor a$

$a \wedge b = b \wedge a$

Identity Elements

$a \lor 0 = a$

$a \wedge 1 = a$

Absorption

$a \lor (a \wedge b) = a$

$a \wedge (a \lor b) = a$

Distributivity

$a \lor (b \wedge c) = (a \lor b) \wedge (a \lor c)$

$a \wedge (b \lor c) = (a \wedge b) \lor (a \wedge c)$

Complements

$a \lor \neg a = 1$

$a \wedge \neg a = 0$

no name yet for the next one

$a = b \wedge a \leftrightarrow a \lor b = b$