(a) Let S be the set of binary strings with the following decomposition: S = ({0}*{11}{1}*)* Explain why this is an ambiguous expression for S. (b) Suppose the weight of a string is its length. Let s(x) be the generating series for S. Suppose we obtain 's(x) by applying the product and sum lemmas for strings using the ambiguous expression in part (a). Which of the following are true? i. For all n 1, [x]s(x) > [x]'s(x). ii. For all n 1, [x]s(x) < [x]'s(x). iii. There exists an n 1 such that [x]s(x) > [x]'s(x). iv. There exists an n 1 such that [x]s(x) < [x] 's(x). Circle all that are true, and briefly justify your answer.