Inference from functional dependencies — evaluate the claim: “Given the dependency R → (S, T), it also follows that R → S.” Decide whether this inference is correct or incorrect.

Introduction / Context: Reasoning with functional dependencies relies on inference rules (Armstrong’s axioms and derived rules). One of the most used rules is decomposition (also called projectivity), which allows splitting a dependency with multiple attributes on the right-hand side.

Given Data / Assumptions:

• We are given R → (S, T), where R, S, and T are attribute sets.
• We assume standard FD semantics and closure rules.
• No special assumptions about keys are needed.

Concept / Approach: The decomposition rule states: If X → YZ then X → Y and X → Z. This follows from reflexivity and augmentation within Armstrong’s axioms. Intuitively, if R determines both S and T together, then R determines S individually (and T individually) as well.

Step-by-Step Solution:

Verification / Alternative check: Compute attribute closure R+ given R → ST: S ∈ R+, T ∈ R+. Hence R → S is implied.

Why Other Options Are Wrong:

• Requiring R → T first is unnecessary; both are simultaneous consequences.
• Key status is irrelevant to the inference.
• Sample data is not required; inference is rule-based.

Common Pitfalls: Thinking combined determination is stronger than individual determination; forgetting standard FD inference rules.

Final Answer: Correct — by the decomposition rule of functional dependencies