Reflexive relation on set of $n$ elements How many reflexive relations are there on a set of $n$ elements? I did the problem and I got the answer $2 ^ {n ^ 2}$. Is it correct? Thanks for the help..!!
Hint: Note that if $X$ is a set with $n$ elements, then there are $n^2-n$ elements in $X\times X$ that are not of the form $\langle x,x\rangle$ for some $x\in X.$ Any, all, or none of these $n^2-n$ elements can be members of a reflexive relation on $X$. (Why?) What about the other $n$ elements of $X\times X$?
$2^{n^2}$ is find for how many number of relations on a set on n elements.
$2^{n(n-1)}$ is find for how many number of reflexive relations on set with $n$ elements.