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  4. Let n(A) = m, and n(B) = n. Then the total number of non-empty relations that can be defined from A to Bis

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Q. Let $n(A) = m$, and $n(B) = n$. Then the total number of non-empty relations that can be defined from $A$ to Bis

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Solution:

Given, $n(A) = m$ and $n(B) = n$
$\therefore $ Total number of relations from $A$ to $B = 2^{mn}$
$\therefore $ Total number of non-empty relations from
$A$ to $B = 2^{mn} - 1$