For a database relation R(a, b, c, d) where the domains of a, b, c, d include…
2013
For a database relation R(a, b, c, d) where the domains of a, b, c, d include only the atomic values. The functional dependency a → c, b → d holds in the following relation
- A.
In 1NF not in 2NF
- B.
In 2NF not in 3NF
- C.
In 3NF
- D.
In 1NF
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Correct answer: A
The relation R(a, b, c, d) satisfies 1NF because all attributes contain atomic values. To determine higher normal forms, we identify the candidate key. Since no functional dependencies exist between a and b, the only way to uniquely determine all attributes is through the combination {a, b}. Thus, {a, b} is the candidate key. The prime attributes are a and b, while c and d are non-prime.\nThe given functional dependencies are a → c and b → d. Here, the non-prime attribute 'c' depends on part of the candidate key ('a'), and 'd' depends on another part ('b'). This constitutes a partial dependency, which violates the requirements of 2NF. Consequently, the relation cannot be in 2NF or any higher normal form like 3NF.",
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