Section $2\mathrm{.}1$ Deterministic Finite Acceptors $($DFA$)$

$(3$ points$)$ Section $2\mathrm{.}1$ Questions $3$ and $4$

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

I. $**$all strings with and even number of $a\text{'}$s

II$.$ All strings with an even number of $a\text{'}$s and an odd number of $b\text{'}$s

III. $**$all strings with exactly one $a$

IV$.$ All strings with at least one $b$ and exactly $2a\text{'}$s