1. (10 points) a. Use Pumping Lemma to prove that DOUBLE(Eo"1 I n 20]) is nonregular. b. Explain the problem in the following attempted proof that STUTTEREO"I" | n 20)) is nonregular: "Proof": In class, we proved that the language (o"1n | n 20 is nonregular. In GroupHW1 we proved that the class of regular languages is closed under the operation STUTTER Applying the contrapositive of this closure claim, we see that STUTTERHOi" | n 2 0) must be nonregular as well Extension (not for credit): How would you prove that STUTTERo"1" | n20) is nonregular? c. Let L be any nonregular set and LF be any finite set. Prove that LULF is nonregular too. Hint: do not use Pumping Lemma. d. Prove that you can't replace union with intersection in the claim above. That is, give an example of a specific nonregular set and a specific finite set whose intersection is regular