4. (15 pt) Let S = {a,b} be an alphabet. Design a DFA that accepts strings whose parts including only a's is of even length. For instance, strings aa and baabaaaa are accepted whereas strings aba and saab are rejected. 5. (15 pt) Design an equivalent NFA for each of the following regular expressions: (a) (babb* +a)* (b)(a +ba)b+aa)*