Problem 4 Suppose L U L2 is regular and L is finite. Show that La is regular Hint: you might want to express L2 as a combination of set operations over L1 UL2 and L1 Problem 5 In the class, we have shown that L = {anb: n > 0} is not regular. Use the pumping lemina to show that Ls = {anbkc" : 712 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