If one attribute is determinant of second, which in turn is determinant of third, then the relation cannot be

Question

Accepted Answer

The correct option is (4):
The relational structure described—where one attribute (let's call it A) determines a second attribute (B), and the second attribute (B) in turn determines a third attribute (C), or $A \to B$ and $B \to C$ — is the precise definition of a **transitive dependency**. The Third Normal Form (3NF) is a foundational rule in database normalization that specifically prohibits this type of dependency. A relation is in 3NF if, and only if, it is in 2NF and there are no non-key attributes transitively dependent on the primary key. Since the scenario explicitly presents a transitive dependency, the relation, by definition, cannot satisfy the requirements of 3NF. Eliminating this redundancy and dependency is the very purpose of normalizing a relation to the Third Normal Form.

The incorrect option is (1):
The term "Well-structured" is an informal and general term used to describe a relation that minimizes redundancy and avoids update, insertion, and deletion anomalies. While a relation in 3NF is typically considered well-structured, a relation containing a transitive dependency, as described in the question, is *not* truly well-structured because it contains redundancy and potential anomalies. However, "Well-structured" is not a formal normal form with specific dependency rules. Therefore, since the question asks for a formal normal form that is explicitly violated, the non-specific and subjective term "Well-structured" is not the best fit for the formal violation of a rule.

The incorrect option is (2):
First Normal Form (1NF) is the most basic level of normalization and only requires that a relation has atomic (indivisible) values in each cell and no repeating groups or nested tables. The existence of a transitive dependency ($A \to B$ and $B \to C$) has absolutely no bearing on whether the attribute values themselves are atomic. The relation could easily have atomic attributes while still containing the transitive dependency. Thus, the relationship between the attributes does not violate the fundamental structural requirement of 1NF.

The incorrect option is (3):
Second Normal Form (2NF) is concerned only with partial dependencies, which occur when a non-key attribute is dependent on only a *part* of a composite primary key. The transitive dependency described ($A \to B \to C$) can exist even if the relation is in 2NF. For instance, if A is the simple primary key (not composite), or if A is a composite key and $A \to B$ is a full functional dependency, the relation would satisfy 2NF but still violate 3NF due to the transitive dependency. Since a relation with a transitive dependency does not inherently violate the rule against partial dependencies, it is incorrect to say the relation cannot be in 2NF.