Question Discussion & Solution

🔑 Key Points

• Boyce-Codd Normal Form (BCNF) is a stronger version of 3NF.
• A relation is in BCNF if and only if for every non-trivial functional dependency \( X \rightarrow Y \), X is a superkey.
• This means that BCNF addresses certain anomalies that 3NF might miss, specifically when a non-prime attribute determines another prime attribute, or when a candidate key is not a superkey.
• BCNF ensures that there are no non-trivial dependencies of an attribute on a proper subset of any candidate key.

📄 Additional Information

• While every relation in BCNF is also in 3NF, the reverse is not always true. A relation can be in 3NF but not in BCNF if it has multiple overlapping candidate keys and non-key attributes determine parts of candidate keys.
• BCNF is generally considered to be an ideal state for many database designs as it fully addresses functional dependencies.
• Higher normal forms like 4NF and 5NF deal with multi-valued and join dependencies, respectively, which are beyond the scope of functional dependencies.

Third Normal Form (3NF) ensures that all non-prime attributes are mutually independent and fully dependent on the primary key.