Provide solutions to the following exercises. Solutions should be in the form of a hand$-$drawn transition

graph $($you may instead use a software tool like the Finite State Machine Designer$).$ Note: Text

descriptions and ASCII images will not be accepted.

For ${\displaystyle \underset{?}{\overset{?}{}}}=\{a$;$b\},$ construct DFAs that accept the sets consisting of

$($a$)$ all strings with exactly one a

$($b$)$ all strings with at least two a$\text{'}$s

$($c$)$ all strings with no more than two a$\text{'}$s

$($d$)$ all strings with at least one b and exactly two a$\text{'}$s

$($e$)$ all strings with exactly two a$\text{'}$s and more than three b$\text{'}$s