Question

In the set of real numbers $R$ which of the following is a not binary operation

• A. $a * b =\frac{a}{b+2}$
• B. $a * b =\sqrt{a^{2}+b^{2}}$
• C. $a * b =\frac{a+2 b}{a^{2}+b^{2}+1}$
• D. $a * b=3 a-2 b$

Answer 1

Answer: (A)

For every $a, b \in R, 3 a-2 b \in R$ (b) (c) are also b.o.
$\therefore a * b =\frac{a}{b+2}$ not a b.o. because $b$ can be $-2$. is a binary operation