Q. 244.5( 4 Votes )

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. nm – 1

C. mn – 1

D. 2mn – 1

Answer :

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


Hence the correct option is (D)

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