On Q, the set of all rational numbers, * is defined by , show that * is not associative.

Question

Philoid · Accepted Answer

Given that * is a binary operation on Q defined by for all a,b∈Q.

We know that associative property is (p*q)*r = p*(q*r)

Let’s check the associativity of given binary operation:

⇒

⇒ ...... (1)

⇒

⇒ ...... (2)

From (1) and (2) we can clearly say that associativity doesn’t hold for the binary operation ‘*’ on ‘Q’.