Question $1$Context$-$free Grammars Consider the alphabet $=\{,,,(,),$ x$,$ y$,$ z$\}$ and the following grammar G $=($V$,,$ R$,$ F$),$ defined by the rules: F $($F $$ F$)|($F $$ F$)|($F$)|$ P P $$ x $|$ y $|$ z $($a$)$ Identify the set of variables and the set of terminal symbols of G$.($b$)$ For each of the following strings si $,$ provide a left$-$most derivation of si in the grammar G $,$ or explain why the string can not be derived G$.$ s$1=((($x $$ z$))($x $$ y$))$ s$2=(($x $$ z$))$ s$3=((($x $$ y$)$ z$))1($c$)$ Consider a modified grammar G$,$ where we remove the brackets $($ and $)$ from the alphabet and the derivation rules. That is we set $=\{,,,$ x$,$ y$,$ z$\}$ and we remove all occurrences of brackets in the derivation rules. Show that there are words that are derived ambiguously in G