Can an equivalence relation contain the null set?

Question

An arbitrary partition $F$, for some equivalence relation $R$, importantly does not contain any set $X$ such that $X = \emptyset$. However, is it possible for a constituent equivalence class, $[x]_R$ to contain the null set? I don't mean this in the sense that $[x]_R = \emptyset$, but whether $\exists [x]_R : \emptyset \subset [x]_R$. If so, will $[x]_R$ be contained in a partition?