Let M $=($Q$,,,$ q$0,$ F$)$ be a DFA, where Q $=\{$q$0,$ q$1,$ q$2,$ q$3,$ q$4\},=\{$a$,$ b$\},$

F $=\{$q$1,$ q$4\},$ and $$ is defined in the following table:

State Input a Input b

q$0$ q$3$ q$0$

q$1$ q$1$ q$2$

q$2$ q$4$ q$2$

q$3$ q$4$ q$1$

q$4$ q$1$ q$4$

i$.$ Draw the transition diagram for M$,$ clearly indicating the start and final

states.

ii$.$ Is bbaaba $$ L$($M$)?$ Why?

Question $2$:

Convert the following regular expression into a NFA:

cbc $($a$*+$ ab$)*$