Normal Form	Removes	Definition (Key Difference)	Lossless Decomposition?	Dependency Preservation?
1NF	Repeating groups / multivalued attributes	Relation has only atomic values (no arrays, no nested sets).	Trivial (just flattening)	Yes
2NF	Partial dependencies	Must be in 1NF AND no non-prime attribute depends on part of a candidate key.	Yes	Yes
3NF	Transitive dependencies	Must be in 2NF AND every non-prime attribute depends directly on a candidate key (no dependency via another non-prime attribute).	Yes	Yes
BCNF	All remaining redundancy from FDs	Must be in 3NF AND for every FD X → Y, X must be a superkey.	Yes	❌ Not always (dependency preservation may be lost)

Example to Illustrate

Suppose relation:

R(StudentID, CourseID, StudentName, DeptID, DeptName)

FDs:

1NF: Relation already atomic.
2NF: Remove partial dependency StudentID → StudentName.
→ Split into: Student(StudentID, StudentName), Enrollment(StudentID, CourseID, DeptID).
3NF: Remove transitive dependency DeptID → DeptName.
→ Split into: Department(DeptID, DeptName), Enrollment(StudentID, CourseID, DeptID).
BCNF: If any FD still has determinant that’s not a superkey (e.g., DeptID → DeptName in some cases), further decomposition is needed.

Key Insights

2NF handles partial dependencies.
3NF handles transitive dependencies.
BCNF handles cases where even in 3NF, determinants aren’t superkeys.
All decompositions are lossless.
Dependency preservation:
- 2NF ✅
- 3NF ✅
- BCNF ❌ (sometimes you lose some dependencies and need to check them by joining relations).