Is the following problem decidable in general:
Given a regular language $R$ and context-free $C$, is every string in $R$ also in $C$? That is, is $L(R)\subseteq L(C)$? What about $L(C)\subseteq L(R)$?
I know that this is decidable if $R$ and $C$ are both regular and undecidable if they are both context free.