The following six questions are adapted from exercise 2.18 of Chapter 2 of Programming Language Pragmatics, by Michael Scott. Consider this context free grammar for a simplified subset of Lisp: S T atom ' S (ST) S T 1. Using this grammar, give the parse tree for the program string (cdr (a b)) $ (note that "cdr", "a", and "b" are each tokenized as "atom"). 2. Find the first set for each of the production rules of this grammar. 3. Find the follow set for each of the production rules of this grammar. 4. Build the parsing table from these first and follow sets. 5. Using the pseudocode from Figure 2.18 of your recommended reading (which will be distributed and discussed in class), show a trace of the stack and the input over time for the string given in question 1.