Theory of Computation

Please solve Section $2\mathrm{.}1$Questions $3,4$ and $7$

Please input the drawings showcasing the final states

Also look at the photo and not the transcribed text

Thank you in advance

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

Section $2\mathrm{.}1$ Question $7$:

Find dfa's for the following languages on $\backslash$Sigma $=\{$a$,$b$\}.$

I. $****$L$=\{$w:$|$w$|$mod$3!=0\}$

II$.$ L$=\{$w:n$\_($b$)($w$)$mod$3>1\}$

III. L$=\{$w:$|$w$|$mod$5=0,|$w$|!=5\}\{$abab$^($n$)$:n$>=0\}\backslash$cup $\{$aba$^($n$)$:n$>=0\}$L$=\{$a$^($n$)$:n$>=0\}\backslash$cup $\{$b$^($n$)$a:n$>=1\}$