Question: If I have regular languages L1 and L2, is the set of strings in L1 but not in L2 also regular? Prove your answer.
Answer: Yes. If L2 is regular then the set of strings not in L2 is also regular. (We proved that the complement of a set is also regular in class.) If L1 and the complement of L2 are regular then their intersection is regular. (We proved the intersection result in class too.) This intersection is the set described in the question.