Question

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

Answer 1

Let a, b ∈ N. Then,

a^b, b^a ∈ N

⇒ a^b + b^a ∈ N      [∵Addition is binary operation on N]

⇒ a ⊙ b ∈ N

Thus, ⊙ is a binary operation on N.