Check the commutativity and associativity of each of the following binary operations: (xi) ‘*’ on N defined by a * b = ab for all a, b ∈ N (xii) ‘*’ on Z defined by a * b = a – b for all a, b ∈ Z

(xi)  to check : commutativity of *

Thus, * is not commutative on N.

to check : associativity of *

Thus, * is not associative on N

(xii)  to check :commutativity of *

Thus, * is not commutative on Z.

to check : associativity of *

Thus, * is not associative on Z