If n ( A ) = 5 and n ( B ) = 7 , then the number of relations on A × B is 2 k , where unit digit of k is

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Solution

Q.
If $n (A) = 5$ and $n (B) = 7$ , then the number of relations on $A \times B$ is $2^{k}$ , where unit digit of $k$ is ________.

Ans.
(5)

$Total number of relations from A to B is 2^{m n} .$

$Here,$ $m = 5, n = 7$ .

$∴$ $Number of relations = 2^{5 \times 7} = 2^{35}$

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