I'm trying to answer this question:
Is it true that for three languages $L_1,L_2,L_3$ such that $L_1 \cap L_2 = L_3$, if $L_1$ and $L_3$ are context free languages, so $L_2$ is context free languages as well.
I know that context free languages are not closed under intersection, but it doesn't mean that there isn't an example for such language. I didn't come with any good idea for languages that fit the question,
Any idea?