L $=\{$w in $\{0,1\}*$: w$$w$$w$$: where $|$w$|=|$w$|$ or $|$w$|=|$w$|\}$

Let's say, we have the following $4$ CFGs labeled as $($A$)$ to $($D$).$

CFG A:

S $->$ RQ $|$ P

P $->0$P$1|1$P$0|\backslash$epsi

Q $->0$Q $|1$Q $|\backslash$epsi

R $->0$R$0|1$R$1|0$R$1|1$R$0|$ Q

CFG B:

S $->$ PR $|$ Q

P $->0$P$0|1$P$1|\backslash$epsi

Q $->0$Q $|1$Q $|\backslash$epsi

R $->0$R$0|1$R$1|0$R$1|1$R$0|$ Q

CFG C:

S $->$ PQ $|$ R

P $->0$P$0|1$P$1|0$P$1|1$P$0|\backslash$epsi

Q $->0$Q $|1$Q $|\backslash$epsi

R $->0$R$0|1$R$1|0$R$1|1$R$0|$ Q

CFG D:

S $->$ PQ $|$ R

P $->0$P$0|1$P$1|0$P$1|1$P$0|\backslash$epsi

Q $->0$Q $|1$Q

R $->0$R$0|1$R$1|0$R$1|1$R$0|$ P

What will be the correct CFG for the language L$?$

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 and C

B and C

C and D

A$,$ B and C

A$,$ B$,$ C and D