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

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

$($b$)$ all strings with at least one a$,$

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

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

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