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Choose the correct alternatives (more than one may be correct) and write the corresponding letters only:

For a context free grammar, FOLLOW(A) is the set of terminals that can appear immediately to the right of non-terminal $A$ in some "sentential" form. We define two sets LFOLLOW(A) and RFOLLOW(A) by replacing the word "sentential" by "left sentential" and "right most sentential" respectively in the definition of FOLLOW (A).

1. FOLLOW(A) and LFOLLOW(A) may be different.
2. FOLLOW(A) and RFOLLOW(A) are always the same.
3. All the three sets are identical.
4. All the three sets are different.
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Consider a Grammar -

$S \rightarrow AB$

$A \rightarrow a$

$B \rightarrow b$

Now only string derivable is $\{ ab \}$.

Let's find Follow(A) in all cases :

1. Follow(A) - set of terminals that can appear immediately to the right of non-terminal $A$ in some "sentential " form
$S \rightarrow AB \rightarrow Ab \rightarrow ab$

Here, we notice only '$b$' can appear to the right of $A$.

Follow$(A) = \{ b \}$

1. LFollow(A) - set of terminals that can appear immediately to the right of non-terminal $A$ in some "left sentential" form
$S \rightarrow AB \rightarrow aB \rightarrow ab$

Here, we notice no terminal  can appear to the right of $A$.

LFollow$(A) = \{\}$

1. RFollow(A) - set of terminals that can appear immediately to the right of non-terminal $A$ in some "right most sentential" form
$S \rightarrow AB \rightarrow Ab \rightarrow ab$

Here, we notice only '$b$' can appear to the right of $A$.

RFollow$(A) = \{ b \}$

edited by
+2
Solving for an instance does not prove the general case, right? Is there some way to prove for the general case?