Determine whether * is a binary operation Which is defined by a * b =

1.	Determine whether * is a binary operation Which is defined by a * b = a + b, a, b ∈ N.
Answer» a * b = a + b, a, b ∈ N Let a & b are arbitrary natural number. Then a + b ∈ N (\(\because\) Sum of natural numbers is natural number) ⇒ a * b ∈ N \(\forall\) a, b ∈ N \(\therefore\) * is a binary operation.

Determine whether * is a binary operation Which is defined by a * b = a + b, a, b ∈ N.

Answer»

a * b = a + b, a, b ∈ N

Let a & b are arbitrary natural number.

Then a + b ∈ N (\(\because\) Sum of natural numbers is natural number)

⇒ a * b ∈ N \(\forall\) a, b ∈ N

\(\therefore\) * is a binary operation.

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Determine whether * is a binary operation Which is defined by a * b = a + b, a, b ∈ N.

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