I've seen the other post (Link) for (b), but I wasn't sure if the same logic applies if you use the assumption below. I also saw this post (Link) for a but again wasn't sure if the assumption might have any effect.
If L(R) ⊆ L(S),
a) R$^*$ + S$^*$ ≡ (R+S)$^*$
b) R$^*$S$^*$ ≡ (RS)$^*$
I think that (a) is true since R is a subset of S, R + S is always in S, thus S$^*$ must include R$^*$ + S$^*$. For (b) I think it is false but I cannot seem to justify it formally due to the assumption. So am I right in saying that a is true and b is false? If so how do I go about justifying that?
(b) is false. Take $R = \emptyset$ and $S = a$, where $a$ is a letter. Then $R \subseteq S$, $R^* = 1$, $R^*S^* = a^*$, but $(RS)^* = \emptyset^* = 1$.