What are the properties of addition and give examples of each property?

Answer 1

Commutative property:

For any two numbers a and b,

a + b = b + a

Associative property:

For any three numbers, a b and c,

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

Other properties, such as the existence of an identity and of an inverse depend on the set over which addition is defined. For example, the first two properties mentioned above are true for addition defined on the set of positive integers, N+. But this set does not include the additive identity (zero), nor the inverse of any element in the set. So the second pair of properties are not general but only when defined over specific sets.