Topic: Database Management Systems
Consider R (A, B, C, D, E, P, G) and the following Functional Dependencies in R:
AB -> CD, DE -> P, C -> E, P -> C, B -> G
Which one of the following is true?
- A. R is in BCNF
- B. R is in 3NF, but not in BCNF
- C. R is in 2NF, but not in 3NF
- D. R is not in 2NF
Answer: D. R is not in 2NF
Explanation: Let's find the candidate keys. The closure of AB is $\{A, B\}^+ = \{A, B, C, D, E, P, G\}$, covering all attributes. Since A and B do not appear on the right side of any functional dependency, they must be part of every candidate key. Thus, AB is the only candidate key. The prime attributes are A and B.
Checking the FDs for normal forms:
The FD B -> G has a proper subset of the candidate key (B) determining a non-prime attribute (G). This is a partial dependency.
Since a partial dependency exists, the relation R violates 2nd Normal Form (2NF). Therefore, R is not in 2NF.