2. (12 points) Define the following languages over {a,b) L = {w E . I the length of w is an integer multiple of 3). For example, E L1, a Li , and bla L1- L2 wE has twice as many as as bs) For example, E L2, a2, bba L2, and babaaa E L2. (a) Design a CFG that generates L 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 (c) ambiguous or not? Justify your answer Note: Using the separator doesn't reduce the number of rules. For example, the grammar (S), a, b),S-aS bS E), S) has three rules