If every non-key attribute is functionally dependent on the primary key, then the relation is in _______.
Second normal form
Understanding Database Normalization and Functional Dependency
Database normalization is a process used in database design to reduce data redundancy and improve data integrity. It involves organizing columns (attributes) and tables (relations) to ensure that dependencies are properly enforced. Normal forms are the different levels of normalization, with each level having specific requirements.
A key concept in normalization is Functional Dependency. A functional dependency exists when the value of one attribute or a set of attributes determines the value of another attribute. We write this as $X \to Y$, meaning attribute(s) $X$ functionally determine attribute(s) $Y$.
The Primary Key of a relation is a minimal set of attributes that uniquely identifies each tuple (row) in that relation.
Exploring Different Normal Forms
Let's look at the conditions for some common normal forms:
- First Normal Form (1NF): A relation is in 1NF if and only if all underlying domains contain only atomic values. This means each cell in the table should contain a single value, not a list or a nested structure, and all entries in a column should be of the same data type.
- Second Normal Form (2NF): A relation is in 2NF if and only if it is in 1NF and every non-key attribute is fully functionally dependent on the primary key. This means that no non-key attribute can be functionally dependent on only a part of the primary key (this is called partial dependency). If the primary key is a single attribute, any relation in 1NF is automatically in 2NF because partial dependency isn't possible. Partial dependency can only occur when the primary key is composite (made of two or more attributes).
- Third Normal Form (3NF): A relation is in 3NF if and only if it is in 2NF and there are no transitive dependencies of non-key attributes on the primary key. A transitive dependency exists if a non-key attribute is dependent on another non-key attribute, which in turn is dependent on the primary key (e.g., PrimaryKey $\to$ NonKeyA $\to$ NonKeyB).
- Fourth Normal Form (4NF): A relation is in 4NF if and only if it is in Boyce-Codd Normal Form (BCNF) and contains no multi-valued dependencies.
Analyzing the Question's Condition
The question states: "If every non-key attribute is functionally dependent on the primary key, then the relation is in _______."
This statement describes a specific condition related to functional dependencies between non-key attributes and the primary key.
- Does it describe 1NF? 1NF deals with atomic values, not the dependency of non-key attributes on the primary key. So, this condition is not the definition of 1NF.
- Does it describe 2NF? The definition of 2NF requires the relation to be in 1NF, and importantly, requires every non-key attribute to be fully functionally dependent on the primary key. The phrasing "functionally dependent on the primary key" in the question, when discussed in the context of different normal forms beyond 1NF, implicitly refers to full functional dependency to distinguish it from partial dependency, which 2NF specifically addresses. A non-key attribute being functionally dependent on the primary key implies either full or partial dependency. The condition for 2NF explicitly rules out partial dependency. Therefore, for a relation already in 1NF, the condition that every non-key attribute is functionally dependent on the primary key, and it satisfies 2NF, means these dependencies must be full dependencies. The question's phrasing perfectly matches the core requirement of 2NF regarding non-key attributes and the primary key after meeting 1NF.
- Does it describe 3NF? 3NF requires being in 2NF and additionally addresses transitive dependencies. The condition in the question only talks about the direct dependency of non-key attributes on the primary key, not indirect dependencies through other non-key attributes. So, this is not the complete definition of 3NF.
- Does it describe 4NF? 4NF deals with multi-valued dependencies, which is a different concept than the functional dependencies described. So, this is not the definition of 4NF.
Based on the definitions, the condition that every non-key attribute is functionally dependent on the primary key, within the context of database normalization, is the defining characteristic of Second Normal Form (2NF) after satisfying 1NF.
Conclusion on Normal Form
The statement "If every non-key attribute is functionally dependent on the primary key" precisely describes the state of a relation that is in Second Normal Form (2NF) relative to its non-key attributes and primary key, assuming it already meets the requirements of 1NF.
Revision Table: Comparing Normal Forms
| Normal Form | Requirements |
|---|---|
| 1NF | Attributes have atomic values. |
| 2NF | In 1NF + No partial functional dependencies (every non-key attribute is fully functionally dependent on the primary key). |
| 3NF | In 2NF + No transitive functional dependencies (of non-key attributes on the primary key). |
| BCNF | Every determinant is a candidate key. |
Additional Information on Database Normalization and Functional Dependency
Understanding functional dependencies is crucial for achieving proper normalization. Partial dependency, which 2NF eliminates, occurs when a non-key attribute depends on only a subset of a composite primary key. For example, in a table (OrderID, ProductID, Quantity, ProductName), if (OrderID, ProductID) is the primary key, but ProductName depends only on ProductID (ProductID $\to$ ProductName), then ProductName is partially dependent on the primary key. 2NF requires eliminating such partial dependencies.
Transitive dependency, addressed by 3NF, occurs when A $\to$ B and B $\to$ C, where A is the primary key and B and C are non-key attributes. For example, in a table (EmployeeID, DepartmentID, DepartmentName), if EmployeeID $\to$ DepartmentID and DepartmentID $\to$ DepartmentName, then DepartmentName is transitively dependent on EmployeeID. 3NF requires removing such dependencies by placing the transitively dependent attributes (like DepartmentName) into a separate table with the intermediate determinant (DepartmentID) as its key.
Important Questions from Normal Form - Teaching
Consider a schema R(A, B, C, D) and following functional dependencies.
A → B
B → C
C → D
D → B
Then decomposition of R into R 1(A, B), R 2(B, C) and R 3(B, D) is _______
Consider a relation R (A, B, C, D, E, F, G, H), where each attribute is atomic, and following functional dependencies exist.
CH → G
A → BC
B → CFH
E → A
F → EG
The relation R is ______.
For a database relation R(a, b, c, d) where the domains of a, b, c, and d include only atomic values, and only the following functional dependencies and those that can be inferred from them hold:
a → c
b → d
The relation is in.Match List I with List II:
List I List II (A) BCNF (I) It removes multivalued dependency (B) 3 NF (II) It is not always dependency preserving (C) 2 NF (III) It removes transitive dependency (D) 4 NF (IV) It removes partial functional dependency Choose the correct answer from the options given below:
In relational database, if a relation R is in BCNF, then which of the following is true about relation R?
