Question

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

Answer 1

Correct Answer - 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`.