$($a$)(3$pts$)$ For each of the following languages give two strings that are members of the language

and two strings that are not. Assume that the alphabet is $\backslash$Sigma $=\{$a$,$ b$\}$

$$ b$$ab$$ab$$

$($a$\backslash$cup ba$\backslash$cup bb$)\backslash$Sigma $(\backslash$epsi $\backslash$cup a$)$b$+$

$($b$)(3$pts$)$ Give a regular expression for the following language over alphabet $\backslash$Sigma $=\{0,1\}$ L$0=\{$w$|$ w contains at least two $1$s and at most one $0\}$

$($c$)(12$pts$)$ Give a regular expression for the following languages. The alphabet is $\{0,1\}.$

$$ L$1=\{$w$|$wbeginswith$1$endswith$0\}$

$$ L$2=\{$w$|$wthelengthofwisatmost$5\}$

$$ L$3=\{$w$|$wstartswitha$1$andhasoddlength,orstartswitha$0$andhasevenlength$\}$ L$4=\{$w$|$ is any string except $0$ and $11\}$

$($d$)(5$pts$)$ Use the procedure described in class to convert the following regular expression to nondeterministic finite automata. You need to show your work and intermediate steps for full credit.

$(0\backslash$cup $01)$

$($e$)(7$pts$)$ Use the procedure described in class to convert the following FAs to regular expressions.

You need to show the intermediate steps for full credit