Which of the following cannot be the number of reflexive relation defined on a set A?

Options

A. 1
B. 4
C. 4096
D. 512

Answer

D

Explanation

We have the number of reflexive relations defined on A is `2^(n^(1)-n)`
Option (a) `rArr2^(n^(2)-n)=2^(@)`
`rArr n(n-1)=1xx0rArrn=1`.
Option (b) `rArr 2x^(n^(2)-n)=2^(2)`
`rArrn(n-1)=2xx1rArrn=2`.
Option (c) `rArr2^(n^(1)-n)=2^(12)`
`rArr n(n-1)=4xx3rArrn=4`.
Option `(d)rArr2^(n^(2)-n)=2^(@)rArrn(n-1)=9`
No integer value of n satisfy the above condition.
`therefore` 512 cannot be the number of reflexive relations defined on a set A.