AUTOMATA THEORYI ONLY NEED # 3, 5 and 6

For each of these problems, describe an algorithm which solves it. (Or, if you think there is no such algorithm, you can prove it.) Don't worry about efficiency of the algorithms. 1) Given a DFA M and a string w, does M accept w? 2) Given a DFA M, is the language M accepts, L(M), infinite? 3) Given a DFA M, is L(M) 0? 4) Given DFAs M, and M2, is L(M) = L(Ma)? 5) Given DFAs M, and M2, is L(M) n L(Ma) = 0? 6) Given DFAs Mi and M2, is L(M C L(M2)? Please submit on elearning solutions to 3, 5, and 6