Functional dependency logic: If attribute A functionally determines both attributes B and C, what else must be true?
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AA → B.
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BB → A.
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CC → A.
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D(B,C) → A.
Answer
Correct Answer: A → B.
Explanation
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:
From the premise: A → B and A → C are both given.Therefore, A → B is necessarily true.No inference supports B → A, C → A, or (B, C) → A without extra assumptions.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.