(a) (5pts) Construct a context free grammar over {a, b, c} whose language is {a^n*b^2n*c^m | n,m>0}

(b) (5pts) Construct a context free grammar over {a, b} whose language is {a^m*b^n | 0nm3n}

(10pts) Write a CFG to generate identifiers (IDs) in the Java Programming Language. An ID in Java is a string of characters consisting of letters (upper-level or lower-level), digits, underscore _ , or dollar sign $. It cannot start with a digit.

(10pts) Using your grammar created in problem 1, give a leftmost derivation, AND draw the tree for the derivation for the identifier $$_1uP .