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Which one of the following statements is FALSE?
- a)Any relation with two attributes is in BCNF.
- b)A relation in which every key has only one attribute is in 2NF.
- c)A prime attribute can be transitively dependent on a key in a 3 NF relation.
- d)A prime attribute can be transitively dependent on a key in a BCNF relation.
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Which one of the following statements is FALSE?a)Any relation with two...
Explanation:
To determine which statement is false, let's analyze each statement one by one.
a) Any relation with two attributes is in BCNF:
This statement is true. BCNF (Boyce-Codd Normal Form) is a higher level of normalization that ensures that all non-trivial functional dependencies are removed from a relation. If a relation has only two attributes, there can be at most one non-trivial functional dependency. Therefore, a relation with two attributes is always in BCNF.
b) A relation in which every key has only one attribute is in 2NF:
This statement is true. 2NF (Second Normal Form) is a level of normalization that ensures that all partial dependencies are removed from a relation. If every key in a relation has only one attribute, it means that there are no partial dependencies present, and hence the relation is in 2NF.
c) A prime attribute can be transitively dependent on a key in a 3NF relation:
This statement is true. 3NF (Third Normal Form) is a level of normalization that ensures that all transitive dependencies are removed from a relation. In a 3NF relation, a prime attribute can be transitively dependent on a key through other non-prime attributes.
d) A prime attribute can be transitively dependent on a key in a BCNF relation:
This statement is false. BCNF is a higher level of normalization than 3NF and it ensures that all non-trivial dependencies are removed from a relation. In BCNF, a prime attribute cannot be transitively dependent on a key through other non-prime attributes. If such a dependency exists, the relation is not in BCNF.
Therefore, the false statement is option 'D'. A prime attribute cannot be transitively dependent on a key in a BCNF relation.
To determine which statement is false, let's analyze each statement one by one.
a) Any relation with two attributes is in BCNF:
This statement is true. BCNF (Boyce-Codd Normal Form) is a higher level of normalization that ensures that all non-trivial functional dependencies are removed from a relation. If a relation has only two attributes, there can be at most one non-trivial functional dependency. Therefore, a relation with two attributes is always in BCNF.
b) A relation in which every key has only one attribute is in 2NF:
This statement is true. 2NF (Second Normal Form) is a level of normalization that ensures that all partial dependencies are removed from a relation. If every key in a relation has only one attribute, it means that there are no partial dependencies present, and hence the relation is in 2NF.
c) A prime attribute can be transitively dependent on a key in a 3NF relation:
This statement is true. 3NF (Third Normal Form) is a level of normalization that ensures that all transitive dependencies are removed from a relation. In a 3NF relation, a prime attribute can be transitively dependent on a key through other non-prime attributes.
d) A prime attribute can be transitively dependent on a key in a BCNF relation:
This statement is false. BCNF is a higher level of normalization than 3NF and it ensures that all non-trivial dependencies are removed from a relation. In BCNF, a prime attribute cannot be transitively dependent on a key through other non-prime attributes. If such a dependency exists, the relation is not in BCNF.
Therefore, the false statement is option 'D'. A prime attribute cannot be transitively dependent on a key in a BCNF relation.
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Community Answer
Which one of the following statements is FALSE?a)Any relation with two...
(1) True, because any relation with 2 attributes is in BCNF.
(2) True, because in 2 NF non-prime attributes should be fully functionally dependent upon keys.
(3) A prime attribute can be functionally dependent on a key in 3 NF.
(4) In BCNF, transitivity is eliminated; hence, statement 4 is false.
(2) True, because in 2 NF non-prime attributes should be fully functionally dependent upon keys.
(3) A prime attribute can be functionally dependent on a key in 3 NF.
(4) In BCNF, transitivity is eliminated; hence, statement 4 is false.
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Which one of the following statements is FALSE?a)Any relation with two attributes is in BCNF.b)A relation in which every key has only one attribute is in 2NF.c)A prime attribute can be transitively dependent on a key in a 3 NF relation.d)A prime attribute can be transitively dependent on a key in a BCNF relation.Correct answer is option 'D'. Can you explain this answer?
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