GATE CS 2025 Set 2 — Question 46
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Databases → Normalization → 1NF, 2NF, 3NF
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Question
Consider the following relational schema along with all the functional dependencies that hold on them.
.Which of the following statement(s) is/are TRUE?
.Which of the following statement(s) is/are TRUE?
Correct answer
(C) R1 is NOT in 3NF; (D) R2 is NOT in 3NF
Solution
To determine if the relations are in 3NF, we first find the candidate keys for each.For
Thus, is the only candidate key.
Thus, is the only candidate key.
R1(A, B, C, D, E) with FDs: 1.Find Candidate Keys: Attributes and do not appear on the right-hand side of any functional dependency. Therefore, they must be part of every candidate key.
(since D → E, then EA → B, then EB → C).Thus, is the only candidate key.
2.Identify Prime and Non-prime Attributes:
- Prime attributes:
- Non-prime attributes:
X → Y, either is a superkey or is a prime attribute.- For
D → E: is not a superkey (it's a proper subset of the key ), and is not a prime attribute. This violates 3NF (and also 2NF).
R2(A, B, C, D) with FDs: 1.Find Candidate Keys: Attribute does not appear on the right-hand side of any functional dependency. Therefore, it must be part of every candidate key.
(since C → A, then A → D and A → B).Thus, is the only candidate key.
2.Identify Prime and Non-prime Attributes:
- Prime attributes:
- Non-prime attributes:
- For
A → D: is not a superkey, and is not a prime attribute. This violates 3NF. - For
A → B: is not a superkey, and is not a prime attribute. This violates 3NF.
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