Exercise 2

Let $\Sigma$ be an alphabet, let L be a language over $\Sigma$ recognized by finite automata and let M be a subset of L. We assume that M is finite whereas L may contain an infinite number of words. We denote by L $\setminus$ M the language obtained by suppressing from L the words of M. Is L $\setminus$ M recognized by finite automata? Justify your answer.