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

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

Let’s check the commutativity of given binary operation:

⇒ a*b = a – b

⇒ b*a = b – a

⇒ b*a≠a*b

∴ Commutative property doesn’t holds for given binary operation ‘*’ on ‘Z’.

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

Let’s check the associativity of given binary operation:

⇒ (a*b)*c = (a – b)*c

⇒ (a*b)*c = (a – b) – c

⇒ (a*b)*c = a – b – c ...... (1)

⇒ a*(b*c) = a*(b – c)

⇒ a*(b*c) = a – (b – c)

⇒ a*(b*c) = a – b + c ...... (2)

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