3. (20pt) Consider the following LL(1) grammar: PE $$ E atom 'E(EEs ) Es EES E (1) Compute: EPS(ES), FIRST(Es), FOLLOW(E), PREDICT(Ess). (2) Give a parse tree for the string (cdr '(a b c)) $$. (3) Show the left-most derivation of (cdr '(a b c)) $$ (4) Show a trace, of a table driven top-down parse of this same input (like the one in Fig.2.21, p.85 of textbook). The end marker $$ is seen as one symbol. Es is one non-terminal symbol. An atom is anything that is different from a list, that is, not between parentheses; examples of atom: car, cdr, a, b