Which of the following statements are TRUE regarding 3NF (Third Normal Form) and BCNF...

BCNF is a stricter form of normalization than 3NF. Every relation satisfying BCNF automatically satisfies 3NF because BCNF eliminates all types of anomalies that 3NF addresses. However, the reverse is not true—a 3NF relation may not be in BCNF. Option B is false because not all 3NF relations are in BCNF. Option C is false because relations can exist in both forms simultaneously. Option D is incorrect; 3NF allows non-prime attributes as long as they depend on the entire primary key (no partial or transitive dependencies).

Step-by-step Derivation:
Recall the definitions:

3NF Definition: A relation is in 3NF if (1) it is in 2NF, and (2) every non-prime attribute is fully functionally dependent on the primary key (no transitive dependencies).

BCNF Definition: A relation is in BCNF if every determinant is a candidate key. This is a stricter condition than 3NF.

Hierarchy: BCNF ⊂ 3NF (BCNF is a subset of 3NF)

Analyze each option:

• A) TRUE: If a relation satisfies BCNF (every determinant is a candidate key), it inherently satisfies 3NF (no transitive dependencies among non-prime attributes). The stricter constraint guarantees the weaker one.
• B) FALSE: Counter-example exists. A relation in 3NF may have a non-candidate-key determinant, violating BCNF.
• C) FALSE: Many relations can be in both 3NF and BCNF simultaneously (e.g., simple relations with only one candidate key).
• D) FALSE: 3NF allows non-prime attributes; the key requirement is no transitive dependencies, not their absence.