Question

The number of binary operations that can be defined on the set $A=\left\{a,b,c\right\}$ is

• A. $3^3$
• B. $3^4$
• C. $3^9$
• D. $9^3$

Answer 1

The correct option is C

$3^9$

Explanation for correct option

The number of binary operations that can be defined on a set of $n$ elements $=n^{n^2}$

Given, $A=\left\{a,b,c\right\}$

Here, number of elements, $n=3$

So the number of binary operation $=3^{3^2}=3^9$

Hence, $\left(\mathrm{C}\right)$ is the correct answer.