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 $A \times B$
$=2^{m n}$
i.e, Total number of non-empty relations is $2^{m n}-1$
Hence, the correct answer is option D.
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