Question

Let S be a finite 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)

$n^{n^{2}}$

Answer 2

Since a binary operation on S is a function from S × S to S, therefore the total number of binary operations on S is the total number of functions from S × S to S, which is $n^{n^{2}}$