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 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 the strings with exactly two $a\text{'}$s and more than three $b\text{'}$s$.$