Q$1.(3$ points$).$ Consider the following NFA M over the alphabet $=\{0,1\}$: Give a regular expression for the language L recognized by M$.$ Use the following order in ripping $($removing$)$ out states: q$1,$ q$2,$ q$3,$ q$4,$ q$5,$ q$0.$ Q$2.(2$ points$).$ For any string w $=$ w$1$w$2$ wn$,$ the reverse of w$,$ written w R$,$ is the string w in reverse order, wn $$ w$2$w$1.$ For any language A$,$ let AR $=\{$w R $|$ w in A$\}.$ For the language L recognized by the machine M in Q$1,$ give an NFA M$$ to recognize L R$.$ Q$3.(3$ points$).$ Convert the following regular expressions to nondeterministic finite automata: $($i$)010(01)+10($ii$)((100)10)10$ Q$4.(2$ points$).$ Use the pumping lemma to show that the language $\{(00)$n$1$ m$(00)$n $|$ m$,$ n $0\}$ is not regular.