Consider a relation with attributes [A, B, C, D] and the following functional…
2024
Consider a relation with attributes [A, B, C, D] and the following functional dependencies: A → B, B → C and C → D. If A is the primary key, which of the following is true regarding BCNF?
- A.
The relation is in BCNF because all determinants are super keys.
- B.
The relation is in 3NF but not in BCNF.
- C.
The relation is not in BCNF.
- D.
The relation is in BCNF because it is in 3NF.
- E.
Question not attempted
Attempted by 390 students.
Show answer & explanation
Correct answer: C
Step 1: Given that A is the primary key, A is a super key. The functional dependencies are A → B, B → C, and C → D.
Step 2: For BCNF, every determinant in a functional dependency must be a super key. Here, A is a super key, so A → B is valid.
Step 3: However, B → C and C → D have determinants B and C, respectively. Since B and C are not super keys (they are not primary keys and not derived from A as super keys), these dependencies violate BCNF.
Step 4: The relation is not in 3NF. 3NF prohibits transitive dependencies for non-prime attributes. A transitive dependency exists if A -> B and B -> C. Since C and D are non-prime attributes being determined by other non-prime attributes (B and C), the 3NF condition is failed.
Step 5: However, BCNF is stricter than 3NF. Since B and C are not super keys, the relation is not in BCNF.