Question

Determine whether the following operation define a binary operation on the given set or not : '*' on N defined by a * b = a + b - 2 for all a, b ∈ N

Answer 1

If a = 1 and b = 1,

a * b = a + b - 2
         = 1 + 1 - 2
         = 0 ∉ N
Thus, there exist a = 1 and b = 1 such that a * b ∉ N

So, * is not a binary operation on N.