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

$($a$)$ all strings of even length.

$($b$)$ all strings of length greater than $5.$

$($c$)$ all strings with an even number of a$\text{'}$s$.$

$($d$)$ all strings with an even number of $a\text{'}$s and an odd number of $b\text{'}$s$.$

For $=\{a,b\},$ construct DFA's graph 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$.$