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


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 $A \times B$

$=2^{m n}$

i.e, Total number of non-empty relations is $2^{m n}-1$

Hence, the correct answer is option D.

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