Let $G$ be the grammar

$S\frac{}{a}bSc|A||$

$A$cAd$|cd.||$

a$)$ Give a derivation of string ababccddcc.

b$)$ Build the derivation tree for the derivation in part $($a$).$

c$)$ Use set notations of $(V,,P,S)$ to define $L(G).$