Axioms and Properties for Multiplication and Addition
if x = y AND y = z, then x = z
Transitive Axiom of Equality
x * 1 = x
Multiplicative Identity Axiom
x * 1/x = 1
Multiplicative Inverse Axiom
-1 * x = -x
Multiplicative Property of -1
x * 0 = 0
Multiplicative Property of 0
x = x
Reflexive Axiom of Equality
if x = y, then y = x
Symmetric Axiom of Equality
if x = y, then x + z = y + z
Addition Property of Equality
x + 0 = x
Additive Identity Axiom
x + -x = 0
Additive Inverse Axiom
(x + y) + z = x + (y + z)
Associative Axiom for Addition
(xy) z = x (yz)
Associative Axiom for Multiplication
x + y = y + x
Commutative Axiom for Addition
xy = yx
Commutative Axiom for Multiplication
x(y +z)= xy + xz
Distributive Axiom for Multiplication over Addition
if x = y, then xz = yz
Multiplication Property of Equality