Question

Let a binary operation ‘*’ be defined on a set A. The operation will be commutative if ________

(a) a*b=b*a

(b) (a*b)*c=a*(b*c)

(c) (b ο c)*a=(b*a) ο (c*a)

(d) a*b=a

This question was addressed to me in my homework.

I want to ask this question from Binary Operations topic in division Relations and Functions of Mathematics – Class 12

Answer 1

Right answer is (a) a*b=b*a

The explanation: A binary operation ‘*’ defined on a set A is said to be commutative only if a*b=b*a, ∀a, b∈A.

If (a*b)*c=a*(b*c), then the operation is said to associative ∀ a, b∈ A.

If (b ο c)*a=(b*a) ο (c*a), then the operation is said to be distributive ∀ a, b, c ∈ A.