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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) nm − 1
(c) mn − 1
(d) 2mn − 1

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Solution

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

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