(30%) For each of the following languages L dentify the distinct residues, and use therm to construct an automaton that recognizes L. Present your automaton as a transition diagram. Label each state, and list separately what is the residue represented by each state. (a) L = {w E {a,b,c)" | #s(w) = 1} (b) L aab) ( nt: there are 5 residues.) (c) L = {w e {a, b)' | #a(w) 2 #b(w)). That is, L consists of the strings where the the alphabet is (a, b). Hi numbers of a's and b's are either both even or both odd