= {a,b}: 1. (9 pts) Consider the following three languages, all subsets of S* where L = {w w is a word such that we is divisible by 3). . L2 = {w w is a word whose length is divisible by 4 }. L3 = {w w is a word such that wla >3}. (a) For each language construct a DFA that recognizes that language. (b) Construct an automaton that recognizes Lin L2. If the constructed automaton is non- deterministic, convert it in a deterministic one. (c) Construct an automaton that recognizes L2 U L3. If the construc'ed automaton is non- deterministic, convert it in a deterministic one