L $=\{$w $\backslash$epsi $\{$a$,$b$,$c$\}*$: a$$b$$c$|$ i$,$ j$,$ k $>=0$ and if i $>$ j then k $=$ i $-$ j$,$ else k $=0\}$

Which of the following CFGs generates L$?$

CFG A:

S $->$ AB $|$ AC

A $->$ aA $|\backslash$epsi

B $->$ bB $|$ b

C $->$ aCc $|\backslash$epsi

CFG B:

S $->$ AB $|$ A

A $->$ aA $|$ a $|\backslash$epsi

B $->$ bBc $|$ b

CFG C:

S $->$ A $|$ B

A $->$ aAb $|$ Ab $|\backslash$epsi

B $->$ aBc $|$ aCc

C $->$ aCb $|\backslash$epsi

CFG D:

S $->$ AB $|$ AC

A $->$ aAb $|\backslash$epsi

B $->$ bB $|\backslash$epsi

C $->$ aCc $|\backslash$epsi

Note, for a language L$,$ the CFG will be correct if and only if it can parse all the strings, w in L$,$ and doesn$$t parse any string, w $$ L$.$

$2$ points

A

B

C

D