Consider a relation R (A, B, C, D, E, F, G, H), where each attribute is…
2024
Consider a relation R (A, B, C, D, E, F, G, H), where each attribute is atomic, and following functional dependencies exist:
CH → G
A → BC
B → CFH
E → A
F → EG
The relation R is ________.
- A.
in 1NF but not in 2NF
- B.
in 2NF but not in 3NF
- C.
in 3NF but not in BCNF
- D.
in BCNF
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Correct answer: A
The relation R is in 1NF but not in 2NF.
1. Candidate Keys:The relation R has four candidate keys: AD, BD, ED, and FD. Attribute D must be included in every candidate key because it does not appear on the right side of any functional dependency, meaning it cannot be determined by any other attributes.
2. Checking for 2NF Violation:For a relation to be in 2NF, it must first be in 1NF (each attribute is atomic) and must not contain any partial dependency (i.e., a non-prime attribute should not depend on a proper subset of any candidate key).
The relation contains multiple partial dependencies:
In A → BC, the subset A determines BC.
In B → CFH, the subset B determines CFH.
In F → EG, the subset F determines EG.
Because these subsets (A, B, and F) are proper subsets of candidate keys like AD, BD, and FD, these are partial dependencies. Therefore, the relation violates 2NF.