# Find the number of elements of reflexive relation on a set of $n$ elements

I do know that $$2^{n^{2}-n}$$ reflexive relations can be created on $$n$$-element set.

The problem:

Relation $$R$$ can be created on $$n$$-element set $$A$$.

if such relation $$R$$ is reflexive, then how many elements should $$R$$ have?

• R should have atleast n elements. – Koro May 20 at 6:18
• A reflexive relation $R$ should have $(x,x) \in R$ for all $x\in A$. Anything else may or may note be in $R$. – Anurag A May 20 at 6:27
• I'm not sure what you want for an answer. Is it a proof that $2^{n^2-n}$ is correct or soemthing else? – Ingix May 20 at 8:44