Section $2\mathrm{.}1$ Deterministic Finite Acceptors $($DFA$)(3$ points$)$ Section $2\mathrm{.}1$ Questions $3$ and $4$ For $\backslash$Sigma $=\{$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 $2$a $\text{'}$s$(3$ 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