$(4$ marks$)$ Using the algorithm mark distinguishable pairs of states that was presented in class on week $4$ and that can be found in the course notes, minimize the number of states

of the DFA depicted in Figure $2.$

Your answer should indicate in detail how you arrived at the solution:

For each stage of the algorithm, indicate which pair$($s$)$ of states are marked as distinguishable at that stage and explain the reason why.

Figure $2$: The DFA to be minimized in Question $4.$

Draw the minimized state diagram where each state is labeled by the corresponding names of states in the original DFA that were merged together.