Consider a relational table R that is in 3NF, but not in BCNF, Which one of the following statements is TRUE?

Question

Consider a relational table R that is in 3NF, but not in BCNF, Which one of the following statements is TRUE?

R has a nontrivial functional dependency X → A, where X is not a superkey and A is a prime attribute.
R has a nontrivial functional dependency X → A, where X is not a superkey and A is a non-prime attribute and X is not a proper subset of any key.
R has a nontrivial functional dependency X → A, where X is not a superkey and A is a non-prime attribute and X is a proper subset of some key.
A cell in R holds a set instead of an atomic value.

LohaHridoy

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2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 1 : R has a nontrivial functional dependency X → A, where X is not a superkey and A is a prime attribute.

Concept:

A relation is in 1NF if every values in the relation are atomic.

A relation R with nontrivial functional dependency X → A, where X is not a superkey and A is a non-prime attribute and X is not a proper subset of any key is in called to be in 2NF.

A relation R with nontrivial functional dependency X → A, where X is not a superkey and A is a prime attribute, is called to be in 3NF.

A relation R with nontrivial functional dependency X → A, where X is a superkey is called to be in BCNF.

Explanation:

Statement I:

corresponds to a relation that is in 3NF but not in BCNF, because for BCNF, X must be a superkey.

Statement II

corresponds to a relation that is only in 2NF by definition.

Statement III

corresponds to a relation that is not even in 2NF. It is in 1NF.

Statement IV corresponds to a relation that is not even in 1NF.