Question:
In a relational data model, which one of the following statements is TRUE?
In a relational data model, which one of the following statements is TRUE?
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A relation with only two attributes will always satisfy the BCNF condition as there are fewer possibilities for violating the condition.
Updated On: Jan 30, 2026
- 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.
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The Correct Option is A
Solution and Explanation
- Option (A) is true. If a relation has only two attributes, it will always be in BCNF. This is because, for a relation to violate BCNF, one of the functional dependencies must involve a non-prime attribute as a determinant, and this condition is automatically satisfied in two-attribute relations.
- 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)
- 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)
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