So, for a course I'm following we got some practice exams to prepare for the finals. However, for some of these we do not have answers, nor can I find someone who is certain of his answer on the following question.
I was hoping someone here can give me some insight to the question(s) listed below.
I figured that when trying to solve (a) I would have to take an arbitrary equivalence class of R and proof that it is also in S. But I am unsure of how to actually formally proof this.
For question (b) I have absolutely no clue, as I originally thought it was false.
Let $R$ and $S$ be two equivalence relations on a finite set U satisfying $R \subseteq S$.
(a) Prove that every equivalence class of R is a subset of an equivalence class of S.
(b) Let $n_R$ be the number of equivalence classes of R and let $n_S$ be the numer of equivalence classes of S. Prove that $n_R \geq n_S$