Question

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

Answer 1

Let a, b ∈ N. Then,

a^b ∈ N      [∵ a^b≠0 and ab is positive integer]

⇒ a * b ∈ N

Therefore,

a * b ∈ N, ∀ a, b ∈ N

Thus, * is a binary operation on N.