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Question

If a set A has n distinct elements, then the number of all relations on A is

A
2n2
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B
n2
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C
2n
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D
2nn
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Solution

The correct option is A 2n2
Let A and B are two sets such that n(A)=a and n(B)=b.
Then, number of relations from A to B is =2n(A)×n(B)=2ab

Hence, number of relations from A to A is 2n(A)×n(A)=2n2

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