Question 41

The grammar productions are:

• $S \rightarrow daT \mid Rf$
• $T \rightarrow aS \mid baT \mid \epsilon$
• $R \rightarrow caTR \mid \epsilon$

Compute FIRST sets:

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

For non-terminal $S$, production $S \rightarrow Rf$ has $\text{FIRST}(Rf) = \{c, f\}$. Thus, $S \rightarrow Rf$ is entered in cell $[S, c]$ (cell 1) and in cell $[S, f]$ (cell 2).

Compute $\text{FOLLOW}(T)$:

• From $S \rightarrow daT$, $\text{FOLLOW}(S) \subseteq \text{FOLLOW}(T)$. Since $S$ is start symbol, $\$ \in \text{FOLLOW}(S)$, so $\$ \in \text{FOLLOW}(T)$.
• From $R \rightarrow caTR$, $\text{FIRST}(R) \setminus \{\epsilon\} = \{c\} \subseteq \text{FOLLOW}(T)$, and $\text{FOLLOW}(R) \subseteq \text{FOLLOW}(T)$.
• From $S \rightarrow Rf$, $f \in \text{FOLLOW}(R)$, which implies $f \in \text{FOLLOW}(T)$.
  Thus $\text{FOLLOW}(T) = \{c, f, \$\}$. Production $T \rightarrow \epsilon$ is placed under all terminals in $\text{FOLLOW}(T)$, so it appears in cell $[T, c]$ (cell 3), in cell $[T, f]$ (already filled in the given table) and in cell $[T, \$]$ (cell 4).

Therefore, the entries are:
(1) $S \rightarrow Rf$, (2) $S \rightarrow Rf$, (3) $T \rightarrow \epsilon$, (4) $T \rightarrow \epsilon$, matching option A.