2) (12 points) For each of the following languages over the alphabet = {a, b), give a DFA that recognizes the language. a) L, = { , b, bb) b) L. = { w e..* I w begins with "ab" and ends with a ab" } c) For any string w , let na(w) denote the number of a's in w. For example ndabbbba)-2. Define the language L,-{ w . I na(w) mod 3-1). d) L,- where L3 is the language in part c). 3) (4 points) Let L = {w e {0, 1)" such that w is a binary representation of an odd integer). Show that L is a regular language. 4) (4 points) Prove that the class of regular languages is closed under complementation. That is if L is a regular language then L is also a regular language. Hint: Use the DFA M that recognizes L to construct a DFA M that recognizes L