For a set $X$, let $R(X)$ be the set of equivalence relations on $X$ and let $P(X)$ be the set of partitions of $X$. Prove there is a bijection $\varphi : R(X) \to P(X)$.
Stuck on how to proceed with this. I understand that equivalence relations and partitions are in essence the same. But in terms of writing a proof, I am really lost how to proceed. Any help will be appreciated.