1. (75 points) For each of the following languages over = {a,b}: Build a DFA that accepts the described language. Explain how the machine works. The drawing of each machine is 10 points. The accompanying "comments are 5 points. (a) The empty set. (b) The empty string. (c) The strings that contain at least one a and end in bb. (d) The strings that start and end with the same symbol. (e) The strings that contain at least one a and do not contain bb. (Suggested strings to test your machine with are: \, a, b, aa, ab, ba, bb, abb, abab, abaab, ababb.)