Provide regular expressions for the following languages.

$($a$)$ L$1=\{$w in $\{0,1\}$

$$

$|$ w contains both $111$ and $0110$ as substrings$\}$

$($b$)$ L$2=\{$a

$3$p$+4$b

q

$|$ p$,$ q in Z

nonneg, q $>=2\}$

$($c$)$ L$3=\{$w in $\{$a$,$ b$\}$

$$

$|$ w does not start with aba$\}$

$[$Note: Make sure that you are thinking about all strings that do not start with aba.$]$

$($d$)$ L$4=\{$w in $\{0,1\}$

$$

$|$ n$0($w$)=1$ and n$1($w$)=3$k for some k in Z

nonneg$\}$

$($e$)$ L$5=\{$w in $\{$a$,$ b$\}$

$$

$|$ w starts with ab and does not have consecutive $$b$$s anywhere$\}$