In relational database normalization, if a relation has no multivalued attributes and no partial dependencies on any candidate key, then in which normal form is the relation considered to be?

Introduction / Context:
This question examines your understanding of relational database normalization, particularly the distinction between first normal form and second normal form. Normalization is used to reduce redundancy and prevent update anomalies. Knowing the exact conditions for each normal form is important when designing or analyzing a relational schema.

Given Data / Assumptions:

- The relation has no multivalued attributes.- There are no partial dependencies on any candidate key.- We are asked to determine the resulting normal form.

Concept / Approach:
First normal form requires that all attribute values be atomic, meaning there are no repeating groups or multivalued attributes. Second normal form builds on first normal form by additionally requiring that no non key attribute is partially dependent on a proper subset of a candidate key. Third normal form further requires that there be no transitive dependencies of non key attributes on candidate keys. The question explicitly states that there are no multivalued attributes and no partial dependencies, which matches the combined requirements for first normal form and second normal form, but does not necessarily guarantee third normal form.

Step-by-Step Solution:
Step 1: No multivalued attributes means the relation satisfies first normal form, since every attribute has single, atomic values.Step 2: The absence of partial dependencies means that no non key attribute depends on part of a composite candidate key.Step 3: Together, first normal form plus the absence of partial dependencies defines second normal form.Step 4: Third normal form additionally requires that no non key attribute depends transitively on a candidate key through another non key attribute.Step 5: The question does not mention transitive dependencies, so we cannot assume that the relation meets third normal form.Step 6: Therefore, the safest and correct conclusion is that the relation is in second normal form.

Verification / Alternative check:
An alternative check is to consult standard definitions. Second normal form is defined as a relation that is in first normal form and has no partial dependencies of non key attributes on any candidate key. Since both of these conditions are given explicitly, second normal form must hold. Nothing is said about transitive dependencies, multivalued dependencies, or higher forms such as Boyce Codd normal form or fourth normal form, so those cannot be concluded from the information given.

Why Other Options Are Wrong:
First normal form alone does not address partial dependencies, so option A is incomplete. Third normal form and Boyce Codd normal form, options C and D, require stronger conditions related to transitive dependencies and key based functional dependencies that are not specified here. Fourth normal form deals with multivalued dependencies and is a higher level of normalization, which again is not implied by the given conditions.

Common Pitfalls:
A common mistake is to jump directly from basic atomic attributes to assuming third normal form without checking for transitive dependencies. Another pitfall is to confuse partial dependency with transitive dependency or to believe that the absence of one automatically implies the absence of the other. Careful reading of definitions and explicit conditions is necessary when identifying normal forms in exam questions and real design scenarios.

Final Answer:
The relation is considered to be in second normal form.