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

Solution

## 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                   = 2mn i.e, Total number of non-empty relations is 2mn−1 Hence, the correct answer is option D.MathematicsRD Sharma XI (2020, 2021)_Volume 1All

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