Consider the following grammar $G$, with $S$ as the start symbol. The grammar $G$ has three incomplete productions denoted by (1), (2), and (3).

$$S \rightarrow d a T \mid \underline{\ (1)}$$

$$T \rightarrow a S \mid b T \mid \ \underline{(2)}$$

$$R \rightarrow \underline{(3)} \mid \epsilon$$

The set of terminals is $\{a, b, c, d, f\}$. The FIRST and FOLLOW sets of the different non-terminals are as follows.

FIRST($S$) = $\{c, d, f\}$, FIRST($T$) = $\{a, b, \epsilon\}$, FIRST($R$) = $\{c, \epsilon\}$

FOLLOW($S$) = FOLLOW($T$) = $\{c, f, \#\}$, FOLLOW($R$) = $\{f\}$

Which one of the following options CORRECTLY fills in the incomplete productions?

Consider the following augmented grammar with {#, @, <, >, a, b, c} as the set of terminals.

S' → S

S → S # cS

S → SS

S → S @

S → < S >

S → a

S → b

S → c

Let I0 = CLOSURE({S' → ∙ S}). The number of items in the set GOTO(GOTO(I0, <), <) is _______

Consider the following context-free grammar where the set of terminals is {a, b, c, d, f}.

S → d a T | R f

T → a S | b a T | ϵ

R → c a T R | ϵ

The following is a partially-filled LL(1) parsing table.

Which one of the following choices represents the correct combination for the numbered cells in the parsing table ("blank" denotes that the corresponding cell is empty)?

Consider the productions A $$ \to $$ PQ and A $$ \to $$ XY. Each of the five non-terminals A, P, Q, X, and Y has two attributes: s is a synthesized attribute, and i is an inherited attribute. Consider the following rules.

Rule 1 : P.i = A.i + 2, Q.i = P.i + A.i, and A.s = P.s + Q.s
Rule 2 : X.i = A.i + Y.s and Y.i = X.s + A.i

Which one of the following is TRUE?