Let R (A, B, C, D, E, P, G) be a relational schema in which the following…
2008
Let R (A, B, C, D, E, P, G) be a relational schema in which the following functional dependencies are known to hold: AB → CD, DE → P, C → E, P → C and B → G. The relational schema R is
- A.
in BCNF
- B.
in 3NF, but not in BCNF
- C.
in 2NF, but not in 3NF
- D.
not in 2NF
Attempted by 245 students.
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Correct answer: D
Summary: The relation is not in 2NF (and therefore not in 3NF or BCNF).
Given functional dependencies: AB → CD, DE → P, C → E, P → C, B → G.
Reasoning:
Compute closure of {A, B}: AB → CD gives C and D; C → E gives E; with D and E, DE → P gives P; B → G gives G. So AB+ contains all attributes, hence AB is a candidate key.
Proper subsets do not form keys: B+ = {B, G} and A+ = {A}, so AB is minimal.
Prime attributes are A and B; all other attributes (C, D, E, P, G) are non-prime.
Check 2NF: there is a functional dependency B → G where B is a proper subset of the candidate key AB and G is non-prime. This is a partial dependency, so the relation violates 2NF.
Since the relation is not in 2NF, it cannot be in 3NF or BCNF.
Conclusion: The relational schema is not in 2NF.