Let $=\{a,b\}$ be the alphabet for this problem. Consider the language

$A=\{a^n{b}^n|n0\},$

and consider the following context$-$free grammar $G$ :

$Slon|aSb.$

Prove that $L(G)=A$ as follows.

$($a$)(5$ points$)$ Show that $S=>{?}^{**}w$ implies winA by induction. HINT: use induction on the

length of the derivation of $w$ from $S.$

$($b$)(5$ points$)$ Show that winA implies $S=>{?}^{**}w$ by induction. Hint: use induction on the

length of $w.$