For sigam $=\{$a$,$b$\},$ construct dfa$$s that accept the sets consisting of

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

$($b$)$ all strings with at least two a$$s

$($c$)$ all string with no more than two a$$s

$($d$)$ all strings with at least one b and exactly two a$$s

$($e$)$ all the strings with exactly two a$$s and more than three b$$s$.$