1. LL Parsing For the following sub-problems, consider the following context-free grammar: S TS TaAa A c (a) What are the terminals and non-terminals of this language? (b) Show the derivation of the string bcacaacabS starting from S (specify which pro- duction you used at each step), and give the parse tree according to that deriva- tion c) Give the first and follow sets for each of the non-terminals of the grammar (d) What are the predict sets for each production? (e) Give the parse table for the grammar. Is this an LL(1) grammar? Why or why not? (f) Show the steps your parser would take to parse "bcacaacab$" (g) Suppose we change rule 5 to A . Is the resulting grammar LL(1)? Why or why not? h) Is the grammar LL(k) for any k