Functional dependency logic: If attribute A functionally determines both attributes B and C, what else must be true?

Introduction / Context:Functional dependencies capture how attributes determine one another. They are central to normalization reasoning and key identification.

Given Data / Assumptions:

• We are told A determines B and A determines C.
• We seek a statement that must be true given this premise.

Concept / Approach:If A determines B and C, then it trivially follows that A determines B. The dependency is one of those explicitly stated. The converse dependencies do not automatically follow without additional information.

Step-by-Step Solution:

Verification / Alternative check:Consider a concrete example. A as a primary key can determine other attributes. That does not imply any non-key attribute determines the key.

Why Other Options Are Wrong:

• B → A or C → A would imply reversal of dependency, which is not guaranteed.
• (B, C) → A also does not follow from A determining B and C.

Common Pitfalls:Assuming determinacy is symmetric. It is not; functional dependency is directional.

Final Answer:A → B.