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. m^{n}

B. n^{m} – 1

C. mn – 1

D. 2^{mn} – 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 = 2^{mn}So, total number of non-empty relations = 2^{mn} – 1

Hence the correct option is (D)

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