In relational database design theory, a transitive dependency is best described as which of the following?

Introduction / Context:
This question focuses on the concept of transitive dependency in relational database normalization. Transitive dependencies are important when deciding whether a relation is in third normal form. Identifying and removing transitive dependencies helps reduce redundancy and update anomalies.

Given Data / Assumptions:

- The term transitive dependency is mentioned.- Options involve different types of functional dependencies and normal forms.- We assume standard textbook definitions of normalization.

Concept / Approach:
A functional dependency X leads to Y is transitive if there exists an attribute set Z such that X determines Z and Z determines Y, and Y is not part of any candidate key. In practice, this often means that a non key attribute depends on another non key attribute, which in turn depends on a key. This situation is undesirable because changes to one non key attribute can cause anomalies in the dependent attribute, and third normal form seeks to remove such dependencies.

Step-by-Step Solution:
Step 1: Recall that in a transitive dependency, a key attribute determines a non key attribute indirectly through another attribute.Step 2: Consider a relation where a primary key determines attribute A, and attribute A determines attribute B, with B being a non key attribute.Step 3: In this case, the key determines B transitively through A, which is a non key attribute.Step 4: Option B describes this situation as one non key attribute depending on another non key attribute through a key attribute.Step 5: Options A and E focus on dependencies only among key attributes, which is not what transitive dependency usually refers to.Step 6: Options C and D discuss normal forms rather than defining the dependency itself.

Verification / Alternative check:
Third normal form definitions state that a relation is in third normal form if it is in second normal form and has no transitive dependencies of non key attributes on candidate keys. Examples typically show attributes such as department name depending on department number, which depends on employee number. Here, employee number is the key, and department name is transitively dependent through department number, a non key attribute. This matches option B.

Why Other Options Are Wrong:
Option A describes a dependency between key attributes, which can exist but is not the usual problem targeted by third normal form. Option C and option D misinterpret transitive dependency as a property of a relation being in first or second normal form, which is incorrect. Option E suggests that transitive dependency involves only candidate keys, which contradicts the emphasis on non key attributes in the standard definition.

Common Pitfalls:
Students sometimes confuse partial dependency with transitive dependency. Partial dependency involves part of a composite key, while transitive dependency involves non key attributes determining other non key attributes. Another pitfall is to remember the term transitive but forget that it specifically concerns non key attributes when considering third normal form.

Final Answer:
A transitive dependency is a functional dependency where one non key attribute depends on another non key attribute through a key attribute.