Recognizing normal forms: If a relation has no multivalued attributes and also contains no partial dependencies (with respect to any candidate key), in which normal form is the relation?

Introduction / Context:
Normalization progresses through successive normal forms, each removing specific sources of redundancy and anomalies. Understanding the criteria for first, second, and higher normal forms helps analysts evaluate schema quality.

Given Data / Assumptions:

• No multivalued attributes (implies 1NF is satisfied: atomic attributes).
• No partial dependencies (non-key attribute depending on part of a composite key).
• Candidate keys may be composite.

Concept / Approach:

First normal form requires atomic (non-repeating) attributes and no repeating groups. Second normal form requires 1NF and additionally prohibits partial dependencies on a proper subset of a candidate key. Since both conditions are met, the relation is in 2NF (though not necessarily 3NF, which also eliminates certain transitive dependencies).

Step-by-Step Solution:

Verification / Alternative check:

Analyze determinants of each non-key attribute; if each depends on the whole key (and attributes are atomic), the relation is at least 2NF.

Why Other Options Are Wrong:

1NF: too weak; we also removed partial dependencies.

3NF/4NF: require additional conditions (transitive dependencies and multivalued dependencies, respectively) not given here.

Common Pitfalls:

Assuming 2NF implies 3NF automatically; overlooking transitive dependencies such as key → attribute1 and attribute1 → attribute2.

Final Answer:

Second normal form