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 $\mathrm{A}=2^{n^{2}}$