Reflexive

a = a

Symmetric

if a = b then b = a

Transitive

if a = b and b = c then a = c

Commutative

a + b = b + a

Commutative

a * b = b * a

Associative

a + (b + c) = (a + b) + c

Associative

a * (b * c) = (a * b) * c

Distributive

a(b + c) = a * b + a * c

Distributive

a(b - c) = a * b - a * c

Additive Identity

a + 0 = a

Multiplicative Identity

a * 1 = a