Which statement(s) is/are correct for a non-recursive predictive parser? Let T…

Concept

Let T be the terminal alphabet. FIRST(γ) ∩ T records terminal symbols that can begin strings derived from γ; ε is added separately when γ is nullable.

FOLLOW(X) ∩ T records terminal symbols that can appear immediately after X in a sentential form; the end marker $ is added separately to the FOLLOW set of the start symbol.

Application

1. In S₁, the witness α ⇒* tβ puts terminal t at the beginning of a string derived from α. This is exactly the condition for t ∈ FIRST(α) ∩ T.

2. In S₂, the witness S ⇒* γXaβ puts terminal a immediately after X in a sentential form derived from S. This is exactly the condition for a ∈ FOLLOW(X) ∩ T.

3. Because both left-hand sides are explicitly intersected with T, the separate ε and $ cases do not affect either terminal-only equality.

Cross-check and contrast

• “Both statements are incorrect” treats the separate ε and $ additions as counterexamples to valid terminal-membership clauses.

• “S₁ is incorrect and S₂ is correct” applies the special-symbol caveat only to FIRST even though FOLLOW also has a separate $ rule.

• “S₁ is correct and S₂ is incorrect” applies the special-symbol caveat only to FOLLOW even though FIRST also has a separate ε rule.

• “Both statements are correct” reads t and a as terminal witnesses in their respective derivations, which matches the two displayed clauses.

Therefore, both statements S₁ and S₂ are correct.