Assignment 7 - Structure: Axioms

a + (-a) = 0

Additive Inverse Property

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

Associative Property of Addition

a(b • c) = (a • b)c

Associative Property of Multiplication

Choose 2 axioms that allows 22 + (m + 8) to be written as m + 30

Commutative - addition, associative - addition

Choose the axiom that allows b(7) to be written 7b

Commutative - multiplication

a + b = b + a

Commutative Property of Addition

a • b = b • a

Commutative Property of Multiplication

a(b + c) = (a • b) + (a • c)

Distributive Property

Axioms are statements about mathematics that require proof. True or false?

False

a + 0 = a

Identity Property of Addition

a • 1 = a

Identity Property of Multiplication

a • 1/a = 1

Multiplicative Inverse Property

A = a

Reflexive Property

Theorems

Statements about mathematics that require proof

Select the property that allows the statement 3 = x to be written x = 3

Symmetric

If a = b, then b = a

Symmetric Property

If a = b and b = c, then a = c

Transitive Property

a • 0 = 0

Zero Property of Multiplication