In a relational data model, which one of the following statements is TRUE?
Show Hint
- A relation with only two attributes is always in BCNF.
- If all attributes of a relation are prime attributes, then the relation is in BCNF.
- Every relation has at least one non-prime attribute.
- BCNF decompositions preserve functional dependencies.
The Correct Option is A
Solution and Explanation
- Option (B) is false. A relation in which all attributes are prime does not necessarily mean it is in BCNF. The BCNF condition is that for every non-trivial functional dependency, the left-hand side must be a superkey. Even if all attributes are prime, if a non-prime attribute determines another non-prime attribute, the relation will not be in BCNF.
- Option (C) is false. Not every relation has at least one non-prime attribute. For instance, if all attributes of the relation are part of the candidate key, then the relation has only prime attributes.
- Option (D) is false. While BCNF decompositions preserve lossless-join and dependency preservation in most cases, they may not always preserve functional dependencies. In some cases, a BCNF decomposition may lose some functional dependencies due to the splitting of relations.
Final Answer: (A)
Top Questions on Normal Forms
- Suppose the following functional dependencies hold on a relation \(U\) with attributes \(P, Q, R, S,\) and \(T\):
\[ P \rightarrow QR, RS \rightarrow T \] Which of the following functional dependencies can be inferred from the above functional dependencies? Consider the relation \(R(P,Q,S,T,X,Y,Z,W)\) with the following functional dependencies:
\[ PQ \rightarrow X; P \rightarrow YX; Q \rightarrow Y; Y \rightarrow ZW \] Consider the decomposition of the relation \(R\) into the constituent relations according to the following two decomposition schemes. \[ \begin{aligned} D_1 &: R = [(P,Q,S,T);\; (P,T,X);\; (Q,Y);\; (Y,Z,W)] \\ D_2 &: R = [(P,Q,S);\; (T,X);\; (Q,Y);\; (Y,Z,W)] \end{aligned} \] Which one of the following options is correct?
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