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

Answer: (A)

We have number of reflexive relations defined on $A$ is $2^{n^2-n}$, where $n$ is the cardinal number of $A$.
Given, $2^{n^2-n}=64\Rightarrow 2^{n^2-n}=2^6$
$\Rightarrow n^2-n=6\Rightarrow n(n-1)=3\times 2$
$\therefore n=3.$