Question

If R is a relation on a finite set having n elements, then the number of relations on A is

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

Answer 1

The correct option is B

$2^{n^2}$

A finite set with n elements Its Cartesian product with itself will have $n^2$ elements.

$\therefore$ Number of relations on $A=2^{n^2}$