[Math] Difference of a regular language and a context-free language

Question

I know that given the context-free language L and the regular language R, the language L \ R is context free. But what about R \ L ? My attempt is as follows:
R \ L = R $\cap$ $\overline{L}$
We cannot know whether $\overline{L}$ is CF or not, so my guess is that we decide whether R \ L is context-free or not.
Am I right? Any help would be appreciated.

Answer 1

HINT:

Since, regular languages are closed under complement property and context-free languages are not closed under complement property.