$(1)$ Write $\backslash$graf code for a DFA M that is @eqnt to N$.$

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:$+$ nfa N

Q$=\{$q$1,$q$2,$q$3,$q$4,$q$5\}$

S$=\{$a$,$b$\}$

q$0=$q$1$

d$($q$1,$a$)=\{$q$2\}$

d$($q$2,\backslash$e$)=\{$q$3\}$

d$($q$2,$b$)=\{$q$1\}$

d$($q$3,\backslash$e$)=\{$q$1\}$

d$($q$3,$b$)=\{$q$4\}$

d$($q$4,$b$)=\{$q$5\}$

d$($q$5,$b$)=\{$q$3\}$

F$=\{$q$3\}$

done.

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