What is the difference between Third Normal Form and BCNF?
Interview preparation resource from Gate Smashers.
BCNF is a stronger (stricter) form of 3NF. In 3NF a functional dependency X -> Y is allowed if X is a super key OR Y is a prime attribute (an attribute that belongs to at least one candidate key). In BCNF every non‑trivial functional dependency X -> Y requires X to be a super key. Therefore every BCNF relation is in 3NF, but a relation can be in 3NF and still violate BCNF. BCNF typically removes more redundancy but decomposing to BCNF can sometimes make it harder to preserve all original functional dependencies.
Core distinction (short)
BCNF is stricter than Third Normal Form. The difference is in the allowed determinants for functional dependencies: 3NF permits a dependency X -> Y when X is a super key or Y is a prime attribute; BCNF requires X to be a super key for every non‑trivial dependency.
Formal rule comparison
State the rules precisely to contrast them.
- 3NF rule: For a functional dependency X -> Y, either X is a super key OR Y is a prime attribute.
- BCNF rule: For a functional dependency X -> Y, X must be a super key (for every non‑trivial FD).
Why a relation can be in 3NF but not BCNF
A prime attribute is an attribute that belongs to at least one candidate key. Because 3NF allows Y to be prime, some dependencies that do not have a super key as determinant are still permitted. That allowance is exactly why a relation can satisfy 3NF yet violate BCNF.
Practical implications and trade-offs
BCNF removes more redundancy because every determinant must uniquely identify a row (be a super key). However, achieving BCNF by decomposing a relation can sometimes make it harder to preserve all original functional dependencies in the decomposed tables. In contrast, 3NF is less strict and is often easier to use when dependency preservation is important.
- Redundancy: 3NF can allow some remaining redundancy; BCNF usually removes more redundancy.
- Dependency preservation: 3NF is often easier to preserve dependencies; BCNF may sacrifice dependency preservation.