Consider the relation schema R(A, B, C, D) and a set of functional…
2022
Consider the relation schema R(A, B, C, D) and a set of functional dependencies F = {A → BC, C → A, B → CD}. Which of the following can be a candidate key of R?
- A.
AB
- B.
A
- C.
ABC
- D.
BCD
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Correct answer: B
Find the Closure of A (A^+):
A^+ = {A}
Apply A -> BC {A, B, C}
Apply B -> CD {A, B, C, D}
Check for Candidate Key Properties:
Since A^+ contains all attributes of the relation, A is a Superkey.
Since A is a single attribute, it is automatically minimal (cannot be reduced further).
Therefore, A is a valid Candidate Key.
Options like AB, ABC, and BCD are superkeys but fail the minimality criteria because their smaller subsets can already derive the entire relation.