Question

Let n(A) = m and n(B) = n. Then the total number of non-empty relations that can be defined from

A to B is
(a) mⁿ
(b) n^m − 1
(c) mn − 1
(d) 2^mn − 1

Answer 1

Let n(A) = m
n(B) = n
since n (A × B ) = mn
where A × B defines A cartesian B.
$\therefore$ Total number of relation from A to B
= number of subsets of A × B
= 2^mn
i.e, Total number of non-empty relations is 2^mn−1
Hence, the correct answer is option D.