1. Let = {a, b}.

(a) Give an example of a language S over such that the language S^* has more six-letter words than seven-letter words.

(b) Give an example of a language S over such that the language S^* has more six-letter words than eight-letter words.

(c) Does there exist an S^* over such that it has more six-letter words than twelve-letter words? Explain briefly why or why not.

*Need not be meaningful words*