Prove that [ContextFreeLanguage - RegularLanguage] is always a context free language, but the opposite is false Let L be a context-free grammar and R a regular language. Show that L-R is always context-free, but R-L is not. Hint: try to connect both automata) 
The above hint did not help me :(

Hints: express $R-L$ more basically in set-theoretic terms. Notice anything about what you get in terms of things you know about CFLs?  Try some very simple $R$ (always a good tactic, at least to start).
