If aSb is a=b (mod 3), then S is indeed the least equivalence relation containing R. Obviously, it has three equivalence classes. Note that for two equivalence relations S' and S'', S' is a subset of S'' iff every equivalence class of S' is a subset of some equivalence class of S''. So, to get an equivalence relation containing S, we can join either two of the the tree or all three classes.