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If the number of reflexive relations def...

If the number of reflexive relations defined on a set A is 64, then the number of elements in A is _____

A

3

B

2

C

6

D

5

Text Solution

Verified by Experts

The correct Answer is:
A
We have number of reflexive relations defined on A is `Z^(n-n)`, where n is the cardinal number of A.
Given, `2^(n^(1)-n)=64rArr2^(n^(2)-n)=2^(6)`
`rArr n^(2)-n=6rArr n(n-1)=3xx2`
`therefore n=3`.
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