Question

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

(a) 2ⁿ
(b) $2^{n^2}$
(c) n²
(d) nⁿ

Answer 1

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

Given : A finite set with n elements
Its Cartesian product with itself will have n² elements.
∴ Number of relations on A = $2^{n^2}$