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) n ²
(d) nⁿ

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) nn

Global Expert · Accepted Answer

(b) 2n2

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

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) nn