This isn't homework.
Prove or dis-prove the statement: If $R$ is a regular language and both $L$ \ $R$ and $L \cup R$ are context-free, then $L$ is context-free.
This isn't homework.
Prove or dis-prove the statement: If $R$ is a regular language and both $L$ \ $R$ and $L \cup R$ are context-free, then $L$ is context-free.
Take $R = A^*$, where $A$ is your alphabet.