Let S be a set and $\{S_\alpha\}$ be nonempty subsets such that S = $\bigcup_{\alpha} $ $S_\alpha$ and $S_\alpha \cap S_\beta$ =$\emptyset $ if $\alpha \neq \beta $ Define an equivalence relation on S in such a way that the $S_\alpha$ are precisely all the equivalence classes.
I don't understand what this is asking. What am I supposed to do?