DBMS Topics
Third Normal Form 3NF
Last Updated : 21 May, 2026
A relation is in Third Normal Form 3NF if:
Definition
A relation is in Third Normal Form (3NF) if:
- It is in 2NF, AND
- No non-prime attribute is transitively dependent on the primary key
A transitive dependency occurs when: PK → X → Y (a non-key attribute Y depends on another non-key attribute X, which itself depends on the PK).
Formal Definition
For every non-trivial FD X → A in R, at least one of the following holds:
- X is a superkey of R, OR
- A is a prime attribute (part of some candidate key)
Identifying Transitive Dependencies
| PK | EmpID |
| EmpID | Name, DeptID, ManagerID ← direct ✓ |
| DeptID | DeptName ← DeptName depends on non-key DeptID ✗ |
| ManagerID | ManagerName ← ManagerName depends on non-key ManagerID ✗ |
| EmpID | DeptID → DeptName (transitive via DeptID) |
| EmpID | ManagerID → ManagerName (transitive via ManagerID) |
Decomposition to 3NF
| Step 1 | Find transitive FDs: |
| DeptID | DeptName |
| ManagerID | ManagerName |
| Step 2: For each transitive FD A | B: |
Another Classic Example
| PK | SID |
| FD: SID | Advisor |
| Advisor | AdvisorDept ← transitive via Advisor ✗ |
Visual Diagram
3NF vs BCNF
3NF allows a FD X → A if A is a prime attribute (part of a candidate key), even if X is not a superkey. BCNF does not allow this exception.
| R(A, B, C) with FDs: AB | C, C → A |
| Candidate keys | {AB}, {BC} |
| C | A: C is not a superkey. But A is prime → OK for 3NF ✓ |
| C | A: violates BCNF (C is not a superkey) ✗ |
Exam Focus
Revise definitions, diagrams, examples, and short-answer points for Third Normal Form 3NF.
Interview Use
Prepare one clear explanation, one practical example, and one common mistake for this DBMS topic.
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