Question

Let $S$ be a set containing $n$ elements. Then the total number of binary operations on $S$ is

• A. $n^n$
• B. ${2^n}^2$
• C. $n^{n^2}$
• D. $n^2$

Answer 1

Answer: (C)

$n^{n^2}$

No of binary operations imply
$S\times S\to S$
$=n(S{)}^{\left[n\right(S\times S\left)\right]}$
$=n^{n\times n}$
$=n^{n^2}$