2. (12 points) Define the following languages over {a, b} 1 = {tpE . I the length of w is an integer multiple of 3} For example, E L1, a Li, and bla E Li. 2 = {te, e . I w has twice as many as as bs} la, bla For example, E L2, a la, and babaaa E L2. (a) Design a CFG that generates L1 and uses fewer than 8 rules. Briefly justify the role of each rule in the grammar. (b) Is the grammar you defined in part (a) ambiguous or not? Justify your answer c) Design a CFG that generates L2 and uses fewer than 5 rules. Briefly justify the role of each rule in the grammar. (d) Is the grammar you defined in part (e) ambiguous or not? Justify your answer S), a, b,SaS | bS | e), S) has three rules. Note: Using the | separator doesn't reduce the number of rules. For example, the grammar