i was reading a proof in a book . There are equivalence relations $R_M$ and $R_L$. The proof showed $R_M \subseteq R_L$ at the end it said because of this we can follow that $Index(R_L) \leq Index(R_M)$.
This is not intuitive to me. Could someone please help me understand. $Index(R)$ is the number of equivalence classes in R.
Saying that $R_M\subseteq R_L$ means that whenever $x\mathrel{R_M}y$, then $x\mathrel{R_L}y$.
Suppose that $A$ is an equivalence class with respect to $R_L$; if $x\in A$, then its equivalence class with respect to $R_M$ is contained in $A$.
Therefore each $R_L$-equivalence class is the union of $R_M$-equivalence classes.