$2$ Consider the following NFAs N$\_1$ and N$\_2$:

Consider the following NFAs N$\_1$ and N $2$:

II

II

i$+$ nfa N$\_1$

$Q=\{q1,q2,q3,q4,q5,q6\}$

$S=\{a,b\}$

$q0=q1$

$d(q1,a)=\{q2\}$

$d(q2,le)=\{q3\}$

$d(q2,a)=\{q1\}$

$d(q3,b)=\{q2,q4\}$

$d(q4,b)=\{q2,q5\}$

$d(q5,a)=\{q6\}$

$d(q6,b)=\{q5\}$

$F=\{q4,q6\}$

done.

II

II

:$+$ nfa N$\_2$

$Q=\{q1,q2,q3,q4\}$

$S=\{a,b\}$

$q0=q1$

$d(q1,b)=\{q1,q3\}$

$d(q2,a)=\{q2,q4\}$

$d(q3,b)=\{q2,q4\}$

$d(q4,b)=\{q3\}$

$F=\{q4\}$

done.

II

$(1)$ Construct a NFA N$\_3$ that recognizes the @lang L$($N$\_1)$UuL$($N$\_2).$ Use the Igraf Simulator to show $2$ strings that are accepted by N$\_3$ and $2$ strings that are rejected by N$\_3.$

$(2)$ Construct a NFA N$\_4$ that recognizes the @lang L$($N$\_1)$@L$($N$\_2).$ Use the Igraf Simulator to show $2$ strings that are accepted by N$\_4$ and $2$ strings that are rejected by N$\_4.$

$(3)$ Construct a NFA N$\_5$ that recognizes the @lang L$($N$\_1)*.$ Use the Igraf Simulator to show $2$ strings that are accepted by N$\_5$ and $2$ strings that are rejected by N$\_5.$