Functional dependency basics:\nEvaluate the claim:\n\n"The functional dependency R → S means that the value of S can be determined when we are given a value of R."

Introduction / Context:
Functional dependencies (FDs) are central to relational theory and normalization. Understanding the precise meaning of R → S helps in designing schemas that minimize redundancy and anomalies (update, insertion, deletion).

Given Data / Assumptions:

• R and S denote attribute sets in a relation schema.
• R → S reads “R functionally determines S.”
• We assume the standard definition used in normalization theory.

Concept / Approach:
By definition, R → S holds if, for any two tuples in the relation with the same values for all attributes of R, those tuples also have the same values for all attributes of S. In practical terms, knowing R fixes (determines) S. This is the basis for identifying keys (e.g., candidate keys where R determines all other attributes) and for decompositions that achieve normal forms (2NF, 3NF, BCNF).

Step-by-Step Solution:

Verification / Alternative check:
Test data for violations: if any two rows share R but disagree on S, the FD does not hold; this motivates constraints and normalization to enforce intended dependencies.

Why Other Options Are Wrong:

• Incorrect: contradicts the formal definition.
• Only for one-to-one: FDs include one-to-many from keys to attributes (key determines many dependent attributes); “one-to-one” is not required.
• Only after normalization: FDs exist regardless of current normal form; normalization uses (not creates) them.

Common Pitfalls:
Confusing FDs with foreign-key relationships; assuming FDs depend on current data samples instead of the intended design rule over all possible tuples; thinking FDs require uniqueness both ways (they don’t—determination is directional).

Final Answer:
Correct