Fpr $=\{a,b\},$ 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 $a^{\text{'}s\text{;}}$

$($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$.$