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

Given: n (A) = m, and n (B) = n

To find: the total number of non-empty relations that can be defined from A to B

Explanation: given n(A) = m and n(B) = n

So n(A×B) = n(A)×n(B) = m×n

And we know a Relation R from a non-empty set A to a non empty set B is a subset of the Cartesian product set A × B.

So total number of relation from A to B = Number of subsets of A×B = 2^mn

So, total number of non-empty relations = 2^mn – 1

Hence the correct option is (D)