Determine Whether of 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

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

योग

If a = 1 and b = 1,

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

So, * is not a binary operation on N.

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Determine Whether of 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