Find the correct functional dependency of a table

Find the correct functional dependencies that satisfy a BCNF table, Which of the following is the correct functional dependencies?

Question:

12. Let us assume a relation R (A, B, C, D, E) that is in BCNF. If BCD is the only key for R, then which of the following functional dependencies is guaranteed to hold for R?

(a) ABCE → D

(b) ABCD → E

(c) BCE → A

(d) None of the above

Answer:

(d) None of the above

Discussion/Reason:

It is given that the relation R is already in BCNF (refer here for rules of BCNF).

That means the left hand side of any functional dependencies that hold in R should be the candidate key. Hence, if the given functional dependencies to be held in R, then the left hand side of given functional dependencies should be BCD.

None of the given FDs have BCD alone in the left hand side. So option (d) is the answer.

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