DBMS Topics
Fourth Normal Form 4NF
Last Updated : 21 May, 2026
A relation R is in Fourth Normal Form 4NF if, for every non-trivial multivalued dependency X →→ Y in R:
Definition
A relation R is in Fourth Normal Form (4NF) if, for every non-trivial multivalued dependency X →→ Y in R:
- X is a superkey of R
4NF builds on BCNF by also eliminating problems caused by multivalued dependencies (MVDs).
Why 4NF is Needed After BCNF
A relation can be in BCNF but still have redundancy caused by MVDs:
| EmpID | Skill | Language |
|---|---|---|
| E001 | Java | English |
| E001 | Java | Hindi |
| E001 | Python | English |
4NF Decomposition
To convert to 4NF, decompose the relation so each MVD is represented in a separate binary relation:
Before (BCNF but NOT 4NF)
Employee(EmpID, Skill, Language)
MVDs: EmpID →→ Skill, EmpID →→ Language
Decompose using each non-trivial MVD
EmpSkills(EmpID, Skill) ← EmpID →→ Skill is now trivial here
EmpLanguages(EmpID, Language) ← EmpID →→ Language is trivial here
After decomposition
+-------+----------+ +-------+----------+
| EmpID | Skill | | EmpID | Language |
+-------+----------+ +-------+----------+
| E001 | Java | | E001 | English |
| E001 | Python | | E001 | Hindi |
+-------+----------+ +-------+----------+
Now adding a new skill only needs 1 row (not 2) ✓
No redundancy ✓
4NF Decomposition Algorithm
WHILE relation R is not in 4NF
Find non-trivial MVD X →→ Y in R where X is NOT a superkey
Decompose R into
R1 = X ∪ Y (X and Y attributes only)
R2 = R − Y (remaining attributes with X)
Replace R with R1 and R2
More Examples
Example 1 — Course Textbook
Example 2 — Project Skills
Checking if Relation is in 4NF
| Step 1 | Check that R is in BCNF. |
| Step 2: Find all MVDs X | → Y in R. |
| Step 3 | For each non-trivial MVD, check if X is a superkey. |
| If yes for all | R is in 4NF. |
| If no for any | R violates 4NF. |
| A trivial MVD: X | → Y where Y ⊆ X OR X ∪ Y = R |
Normal Form Hierarchy Including 4NF
Summary
| Eliminates | |
|---|---|
| BCNF | Redundancy from functional dependencies |
| 4NF | Redundancy from multivalued dependencies |
| 5NF | Redundancy from join dependencies |
Most real-world database designs target BCNF or 3NF. 4NF and 5NF are theoretically important but less commonly applied in practice.
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