$(8$ points$)$ On $=\{a,b\}.$

Draw the NFA figure defined by:

$(q0,a)=\{q0\}$

$(q0,b)=\{q1\}$

$(q1,b)=\{q1,q2\}$

$(q2,a)=\{q1,q3\}$

$(q3,b)=\{q3\}$

$(q1,)=\{q0\}$

$(q3,)=\{q1\}$

q $0$ is the initial state and q $2$ is the final$($accepting$)$ state

$(10$ points$)$ Convert the NFA from question $5$ to a DFA $($show all your work$)$