Question

Let ‘*’ be defined on the set N. Which of the following are both commutative and associative?

(a) a*b=a+b

(b) a*b=a-b

(c) a*b=ab^2

(d) a*b=a^b

The question was posed to me in an online quiz.

Enquiry is from Binary Operations in division Relations and Functions of Mathematics – Class 12

Answer 1

Correct answer is (a) a*b=a+b

For explanation I would say: The binary operation ‘*’ is both commutative and associative for a*b=a+b.

The operation is commutative on a*b=a+b because a+b=b+a.

The operation is associative on a*b=a+b because (a+b)+c=a+(b+c).