1.Intuitively pumping lemmas for regular languages and context-free languages are correct. Explain your intuition. Your explanation must make sense. (20 pts) 2.Prove that the following language L is not context free: 25 pts) 3.Describe a pushdown automaton (PDA) to recognize the following language: (25 pts) L={ww,e I w in (a lb). } Show the transition function and how it works on this language. Apply your PDA on the string abba and see how it works 4.Show that CFLs are closed under union, concatenation, and Kleine star closure, but they are not closed under intersection. (25 pts) 5.Show that CFLs are not closed under complementation( pts)