Question $3(3$pts$)$

You probably remember this little language $($and maybe you$$re tired of seeing it$)$:

$\backslash$Sigma $=\{$a$,$b$\}$

$$ L $=\{$ab$,$aab,aaab,...$\}$

It$$s not a super exciting pattern, and it$$s definitely a regular language. That doesn$$t mean we can$$t provide a context free grammar for it$,$ though.

$($a$)$ First, provide a context free grammar for this language that is not also regular. $($b$)$ Then, explain why it is context free but not regular.

Hint: Remember that every regular grammar is context free, but not every context free grammar is regular. For part $($a$),$ you$$ll need to break the game$-$rules that make something a "regular grammar". For part $($b$),$ you$$ll have to talk about the shape of the rules you used.