Question

On the set of all natural numbers $N$, which one of the following $*$ is a binary operation ?

• A. $a * b = 3a - 4b$
• B. $a * b = \sqrt {ab}$
• C. $a*b=\frac {a-b}{a+b}$
• D. $a * b = a + 3b$

Answer 1

Answer: (D)

$a * b = a + 3b$

Answer 2

Since, $a, b \in N$, $\therefore a^{*} b=a+3 b \in N$