Theory of Computation please solve all questions 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 $2\mathrm{.}1$ Question $7$: $($The answer to III is at the bottom of this document$)$ 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$>=1$ Thi$(3$ points$)$Section $2\mathrm{.}1$ Question $7$: $($The answer to III is at the bottom of this document$)$

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

I. $****L=\{w$:$|w|mod30\}$

II$.L=\{w$:$n_b(w)mod3>1\}$

III. $L=\{w$:$|w|mod5=0,|w|5\}$