Problem 5 In the class, we have shown that L-(a" : n 20 is not regular. Use the pumping lemma to show that L3 = {angen : n 0, k n) is not regular. Can you prove by a simpler way using homomorphism? Problem 6 Show that there exists a non-regular language that satisfies the pumping lemma. In particular, you can consider the following language. You need to show that (1) L is not regular, and (2) L satisfies the pumping lemma