$1.$ For $=\{$a; b$\},$ construct DFAs that accept the sets consisting of

$($a$)$ all strings of odd length

$($b$)$ all strings of even length

$($c$)$ all strings of length greater than $5$

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

$($e$)$ all strings with an even number of a$$s and an odd number of b$$s