Let $L=\{\begin{array}{ccc}\text{w}\text{i}\text{n}& \{a,& b{\}}^{**}\text{:}{n}_a(w)1\\ n_b(w)=2\end{array}$

$\}$ Let M$1,$ M$2,$ M$3,$ M$4$ be the following

NFAs. For each NFA determine whether

or not the NFA accepts L$.$ If the NFA does

not accept $L,$ give a string that is in $L$ that

is not accepted by the NFA.

M$1$

a$.$ Does $L(M1)=L?$ If $L(M1)M$ then

find a string $w$ that belongs to $L$ that is

not accepted by M$1.$

M$2$

b$.$ Does $L(M2)=L?$ If $L(M2)L$ then

find a string $w$ that belongs to $L$ that is

not accepted by M$2.$

${?}^{{?}^{?}}{?}^{{?}^{?}}2$

c$.$ Does $L(M3)=L?$ If $L(M3)M$ then

find a string $w$ that belongs to $L$ that is

not accepted by M$3.$

M$4$

d$.$ Does $L(M4)=L?$ If $L(M4)M$ then

find a string $w$ that belongs to $L(M4)$ but

does not belong to $L.$