$[10]$ For a context$-$sensitive grammar G $=($V$,$ T$,$ S$,$ P$)$where V $=\{$S$,$ A$,$ B$,$ C$\},$ T $=\{$a$,$ b$,$ c$\},$ and

$$ P $=\{$ S $$ SABC $|$ ABC,$$

$$ AB $$ BA$,$ AC $$ CA$,$ BA $$ AB$,$ BC $$ CB$,$ CA $$ AC$,$ CB $$ BC$,$

$$A $$ a$,$ B $$ b$,$ C $$ c $\}$

$(1)[5]$ Give the language, L$($G$),$ in a formal expression, including the relational operator in the length of strings.$$ e$.$g$.)$ L$($G$)=\{$w$|$ #$($a$)<$ #$($b$)$ in w$\}\{$ w$|$ #$($a$)=$ #$($b$)=$ #$($c$)$ in w $\}$