Check the commutativity and associativity of each of the following binary operations: ‘*’ on Q defined by a*b = ab/4 for all a,b ∈ Q

Question

Philoid · Accepted Answer

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

We know that commutative property is p*q = q*p, where * is a binary operation.

Let’s check the commutativity of given binary operation:

⇒

⇒ b*a = a*b

∴ Commutative property holds for given binary operation ‘*’ on ‘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’.