On the set Q of all rational numbers if a binary operation * is defined by , prove that * is associative on Q.
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 hold for the binary operation ‘*’ on ‘Q’.