If $A = {a, b, c, d, e}$ and $B = {1, 2, 3}$ , then the total number of non-empty relations from $A$ to $B$ is

5^{3} - 1

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3^{5} - 1

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2^{3 \times 5} - 1

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3 \times 5 - 1

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Solution

The correct option is C $2^{3 \times 5} - 1$
Total number of relations $= 2^{3 \times 5}$ , which contains empty set too.
$∴$ Total number of non-empty relations from $A$ to $B$ will be $2^{15} - 1$

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