For a database relation R(A, B, C, D) where the domains of A, B, C and D…
20172018
For a database relation R(A, B, C, D) where the domains of A, B, C and D include only atomic values, only the following functional dependencies and those that can be inferred from them are :
A → C
B → D
The relation R is in _______.
- A.
First normal form but not in second normal form.
- B.
Both in first normal form as well as in second normal form.
- C.
Second normal form but not in third normal form.
- D.
Both in second normal form as well as in third normal form.
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Correct answer: A
Answer: The relation is in first normal form but not in second normal form.
Reasoning:
Candidate key: {A, B} is a candidate key because (A,B)+ = {A, B, C, D} using A→C and B→D.
Prime and non-prime attributes: A and B are prime (part of a candidate key); C and D are non-prime.
Partial dependencies: A→C and B→D are dependencies where a proper subset of the candidate key (A or B) determines a non-prime attribute (C or D). This violates second normal form (2NF).
Conclusion: The relation satisfies 1NF (atomic domains) but does not satisfy 2NF, and therefore it is not in higher normal forms that require 2NF.
Normalization suggestion: Decompose to remove partial dependencies, for example into R1(A,C) with key A and R2(B,D) with key B (and include R3(A,B) if you need to preserve the association between A and B).
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