Consider the following context-free grammar where the set of terminals is $\{a, b, c, d, f\}$. $$\begin{aligned} S &\to d a T \mid R f \\ T &\to a S \mid b a T \mid \epsilon \\ R &\to c a T R \mid \epsilon \end{aligned}$$ 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)?

To fill the LL(1) parsing table, we compute the $\text{FIRST}$ and $\text{FOLLOW}$ sets for each non-terminal.

### 1. FIRST Sets:

• $\text{FIRST}(R) = \{c, \epsilon\}$

• $\text{FIRST}(T) = \{a, b, \epsilon\}$

• $\text{FIRST}(S) = \{d\} \cup \text{FIRST}(R f) = \{d\} \cup \{c, f\} = \{c, d, f\}$

### 2. FOLLOW Sets:

• Since $S$ is the start symbol, \\ \in $\text{FOLLOW}$(S)$.

• From $T \to a S$, $\text{FOLLOW}(S)$ contains $\text{FOLLOW}(T)$.

• From $S \to R f$, $\text{FOLLOW}(R) = \{f\}$.

• From $R \to c a T R$, $\text{FOLLOW}(T)$ contains $(\text{FIRST}(R) \setminus \{\epsilon\}) \cup \text{FOLLOW}(R) = \{c\} \cup \{f\} = \{c, f\}$.

• From $S \to d a T$, $\text{FOLLOW}(T)$ contains $\text{FOLLOW}(S)$. Thus, \\ \in $\text{FOLLOW}$(T)$.

• Therefore, \text{FOLLOW}(T) = \{c, f, \\}$and$$\text{FOLLOW}$(S) = \{c, f, \$\}.

### 3. Parsing Table Entries:

• For production $S \to R f$:

  $$\text{FIRST}(R f) = \{c, f\}$$

  This production is placed in $M[S, c]$ (cell ①) and $M[S, f]$ (cell ②).

  • Cell ① = $S \to R f$

  • Cell ② = $S \to R f$

• For production $T \to \epsilon$:

  $$\text{FOLLOW}(T) = \{c, f, \$\}$$

  This production is placed in $M[T, c]$ (cell ③), $M[T, f]$, and M[T, \]$ (cell ④).

  • Cell ③ = $T \to \epsilon$

  • Cell ④ = $T \to \epsilon$

Thus, the correct combination is given by Option (A).