Question $18$

G$4$ is a context$-$free grammar $G4=(V=\{A\},{\displaystyle \underset{?}{\overset{?}{}}}=\{0,1,2\},R,A)$ whose rules are

defined below:

AlongrightarrowA$012|0A12|01A2|$

The grammar above was designed to generate the following language

all words that contain equal numbers of $0s,1s$ and $2s$

What alternative is true about G$4?$

G$4$ is not a CFG for L$4$ because it should not allow the empty string and it should add a new rule

generating string $012$

G$4$ is a correct CFG for L$4$ because it takes into account all possible combinations of Os$,1s$ and $2s$

G$4$ is not a CFG for L$4$ because it is incomplete

G$4$ is a correct CFG for $L4$ because it matches the description of $L4$