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..!!
2026-04-11 21:53:43.1775944423
Reflexive relation on set of $n$ elements
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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 $X\times X$?