If R is a relation on a finite set having n elements,
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) $n^{n}$

Solution:

(b) $2^{n^{2}}$

Given : A finite set with n elements

Its Cartesian product with itself will have n2  elements.

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