Transitive dependency in 3NF 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).
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.