Linz Section $2\mathrm{.}1$

For ${\displaystyle \underset{?}{\overset{?}{}}}=\{a$;$b\},$ 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$\text{'}$s and an odd number of b$\text{'}$s