Question

Name the addition property illustrated by each of the following examples:

A + (B + C) = (A + B) + C property

A + B = B + A property

A + (−A) = 0 property

A + 0 = A property

Answer 1

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Explanation:

A + (B + C) = (A + B) + C : associative property

A + B = B + A : commutative property

A + (−A) = 0 : inverse property

A + 0 = A : identity property

Answer 2

(i) Associative property of addition.

(ii) Commutative property of addition.

(iii) Inverse property of addition.

(iv) Identity property of addition.

Explanation:

Associative property of addition: If a, b and c are three number, then

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

Commutative property of addition: If a and b are two number, then

`a+b=b+a`

Inverse property of addition: The sum of a number and its additive inverse (-a) is 0.

`a+(-a)=0`

Identity property of addition: The sum of a number and identity element 0 is the same number.

`a+0=a`

By using the above definitions we can say that

(i) A + (B + C) = (A + B) + C is Associative property of addition.

(ii) A + B = B + A is Commutative property of addition.

(iii) A + (−A) = 0 is Inverse property of addition.

(iv) A + 0 = A is Identity property of addition.