# Context Free Languages

Let $F$ be a finite language, and $L$ an arbitrary language. Show that if $L$ is context-free, then so is $L-F$.

How would one prove this? Is it possible?

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This answer to an earlier, more general question outlines a proof using automata. –  Brian M. Scott May 30 '12 at 4:46
@BrianM.Scott Intuitively what's on that post makes sense but I don't know how to build a solution to this question out of it. –  Jack Kobil May 30 '12 at 4:56
Are you familiar with pushdown and finite state automata as recognizers of context-free and regular languages? –  Brian M. Scott May 30 '12 at 4:58
@BrianM.Scott yes, to some extent. –  Jack Kobil May 30 '12 at 5:02
@BrianM.Scott such as a language is able to be generated by a context-free grammar if a pushdown automaton can be made to accept it. Is that what you're referring too? And all regular languages have a corresponding context free grammar. –  Jack Kobil May 30 '12 at 5:04