Let L = {w {A Z, , , , ,(,)}* : w is a syntactically legal Boolean expression}.

(a) Write an unambiguous context-free grammar that generates L. The grammar should both: use the following precedence levels to the operators (from highest to lowest): , , , and ; associate left given operators of equal precedence (if an operator is left-associative, then A B C is interpreted as (A B) C).

(b) Show the parse tree that your grammar will produce for the string: A B (A B A)