Question

Determine whether the following operation define a binary operation on the given set or not : 'O' on Z defined by a O b = a^b for all a, b ∈ Z.

Answer 1

Both a = 3 and b = -1 belong to Z.

⇒ a * b = 3^-1

             =`1/3` ∉ Z

Thus, * is not a binary operation on  Z.