3. (21 pts) For each of the following languages, write a grammar that describes the language. (a) (7 pts) The set of strings over alphabet fa, b) that begin with at least two a's, and end with at least two b's (same language as above). (b) (7 pts) The set of strings that consist of an even number of a's, over alphabet fa (c) (7 pts) The set of strings of parentheses (), brackets [], and braces {\ that are properly nested. For instance, ()I)is properly nested, while ([)] is not. 4. (20 pts) Consider the following grammar for Scheme: expr ATOM I list list - (exprs) exprs--> expr exprs l Using this grammar, show a parse tree for the expression (lambda (a) a a)). Does the language described by this grammar contain a finite number of strings? If so, why? If not, why not