Additive Identity Property
a + 0 = a, 0 + a = a
Multiplicative Identity Property
a1 = a, 1a = a
Multiplicative Property of Zero
a0 = 0, 0a = 0
Multiplicative Inverse Property
a/b * b/a = 1
Reflexive Property of Equality
a = a
Symmetric Property of Equality
If a = b, then b = a.
Transitive Property of Equality
If a = b and b = c, then a = c.
Substitution Property of Equality
If a = b, then a may be replaced by b in any expression.
A set is closed under an operation if and only if the operation on two elements of the set produces another element of the set. If an element outside the set is produced, then the operation is not closed.
a(b + c) = ab + bc, a(b - c) = ab - ac
a + b = b + a, ab = ba
(a + b) + c = a + (b + c), (ab)c = a(bc)