$2(4$ points$)$ Let $=\{a,b\},L_1=\{wbab|win{}^{**}\}.$

Draw the state diagram of a DFA that accepts the complement of $L_1.$ Your state diagram should contain only four states.

$3(4$ points$)$ Draw the state diagram of a DFA that accepts the language of all strings over $\{a,b\}$ that contain the sub$-$string bab or the sub$-$string aba.Your finite automaton should not be overly complicated.

$4(3$ points$)$ Give the $5-$tuple definition of your DFA from problem $3.$