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Came across this question : State whether True or False

A prime attribute can be transitively dependent on a key in 3NF

Answer: True
How could this be true? Because as far as I know, A relation initially in 1NF is said to be in 3NF when partial and transitive dependencies have been eliminated. Correct me if I'm wrong.

Also, would it be correct to say that given a relation which doesn't have any non prime attribute along with no partial dependencies, then the relation is in BCNF ?
(I don't have any knowledge beyond BCNF).

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An accepted definition of Third Normal Form is that any non-trivial dependency with a single attribute on the right part must have a superkey as left part, or the right part must be constituted by a prime attribute.

In other words, if you have a dependency with a prime attribute on the right part, that dependency does not violates the 3NF.

For your second question, a relation is in BCNF if any non-trivial dependency has a superkey as left part. If a relation does not have partial dependencies, and all the attributes are prime, this means that no dependency exists with attributes that are not a full key or that are not constituted by non-prime attributes. So, the answer is yes, that relation is in BCNF.

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  • $\begingroup$ Done with second question. But, the definition you stated for 3NF is I suppose actually of BCNF, as stated by Wikipedia : If a relational schema is in BCNF then all redundancy based on functional dependency has been removed, although other types of redundancy may still exist. A relational schema R is in Boyce–Codd normal form if and only if for every one of its dependencies X → Y, at least one of the following conditions hold:[2] X → Y is a trivial functional dependency (Y ⊆ X) X is a superkey for schema R $\endgroup$
    – virmis_007
    Jan 26, 2018 at 16:27
  • $\begingroup$ The condition for BCNF is that for each non-trivial dependency X -> A, X is a superkey. The condition for 3NF is that for each non-trivial dependency X -> A, either X is a superkey or A is prime. These definitions can be found on any good book on databases. $\endgroup$
    – Renzo
    Jan 26, 2018 at 22:10

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