Question $4(30$ points$)$: Design a

context free grammar for each language

below:

$(1)L=\{\begin{array}{c}w\end{array}$ in $\{a,b{\}}^{**}|w||$ has at least two $\{$:$a^{\text{'}}s\}.$

$(2)L=\{\begin{array}{c}w\end{array}$ in $\{a,b{\}}^{**}|w||$ does not have ab as

its substring$\}.$

$(3)L=\{\begin{array}{c}w\end{array}$ in $\{a,b{\}}^{**}|w||$ starts with a and

has at least two b$\text{'}$s$\}.$