3. Give a constructive proof to show that a DFA Dk=(Qk,k,k,q0,Fk) exists that recognizes each Lk={w:w ends in k1 's } (for all k>0 ) over ={0,1. 4. Each of the following languages are composed of two simpler languages over the alphabet ={a,b,c}. For both, construct the DFA's for the simpler languages, then combine them using the construction of the closure proof presented in lecture (and page 46 of text): a. {w:w starts with a and has at most one b} b. {w:w has an odd number of b 's or ends in c}