$(12)$ Let Lsube${}^{***}$ be a regular language. Then there is an NFA $M=(Q,$;$,{}_{ti},F^{\text{'}})$ that recognizes the language $L.$ But we want an NFA for the language $\frac{?}{\text{b}\text{a}\text{r}}(L).$ So we build an NFA $M^{\text{'}}=(Q,,,q_0,\frac{Q}{\frac{?}{?}}{F}^{\text{'}}).$ This does not seem to work in general. To show this,

$($a$)$ Give an example of an NFA $M$ for which $L(M)su\frac{b}{b}ar(L(M^{\text{'}})).$

$($b$)$ Give an example of an NFA $M$ for which $L(M)\frac{?}{b}=ar(L(M^{\text{'}})).$

$($c$)$ Give an example of an NFA $M$ for which $L(M)su\frac{p}{b}ar(L(M^{\text{'}})).$