# Can anyone help me understand the following paragraph?

I was reading Database Systems Design, Implementation and Management by Carlos Coronel. In the chapter of `Normalization` after he explained 3NF, he writes

The existence of multiple candidate keys can also influence the identification of transitive dependencies. Previously, a transitive dependency was defined to exist when one nonprime attribute determined another nonprime attribute. In the presence of multiple candidate keys, the definition of a nonprime attribute as an attribute that is not a part of any candidate key is critical. If the determinant of a functional dependence is not the primary key but is a part of another candidate key, then it is not a nonprime attribute and does not signal the presence of a transitive dependency.

I am having hard time to understand what he wants to say. Can anyone explain this paragraph in simpler terms.

I do not know if the following can be useful to explain the involuted phrase that you cited, however all the following facts are true.

1. A relation must have at least a candidate key and can have more then one candidate key.

2. By definition, an attribute is prime if it is part of any candidate key.

3. A transitive dependency is a dependency that derives from two other dependencies through the “transitive” Armstrong’s axiom (if X -> Y and Y -> Z, then X -> Z), so for instance if in a relation R(A, B, C, D) we have that A -> BC and BC -> D, the dependency A -> D is a transitive dependency.

4. A transitive dependency can be problematic (that is can produces data anomalies) if the second dependency of the transitive rule (the “Y -> Z” dependency of the rule) has a determinant which is not a full candidate key, but (a) a subset of a candidate key, or (b) contains attributes that are not prime.

Consider the relation R(A, B, C, D E), with dependencies AB -> CDE, CD -> ABE, C -> E. In this case there are two candidate keys, AB and CD, so C, the determinant of C -> D, is a prime attribute, since it is an attribute of the candidate key CD (“it is not a nonprime attribute”).

Note that in the previous example the attribute E is transitively dependent from AB (from AB -> CDE we can derive AB -> C, and from AB -> C and C -> E, we can derive AB -> E) and the relation is not in 3NF, neither in BCNF.

• I think your last example is not even in 2NF. Oct 13, 2018 at 16:26
• @ypercubeᵀᴹ yes the example is not even in 2NF because C -> E is a partial dependency because since C is a prime attribute and subset of candidate key CD and determines E a non prime attribute. Am i right? Oct 13, 2018 at 17:03
• @ypercubeᵀᴹ and Jot Waraich, yes, the relation is neither in 2NF. Oct 13, 2018 at 18:22