GATE CS 2025 Set 1 — Question 47
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Databases → Normalization → 1NF, 2NF, 3NF
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Question
Consider a relational schema , with functional dependencies .
The relation is decomposed into two relations, and . Which of the following statement(s) is/are TRUE?
The relation is decomposed into two relations, and . Which of the following statement(s) is/are TRUE?
Correct answer
(B) The relations t1 and t2 are in BCNF.; (C) The decomposition constitutes a lossless join.
Solution
1.Analyze the original relation :
- Functional Dependencies (FDs):
N → CandN → O. - Candidate Key: (since ).
- Normal Form Check: For both FDs, the left-hand side () is a superkey. Therefore, the relation is in BCNF (and consequently in 3NF). Statements (A) and (D) are FALSE.
- with FD
N → C. Key is . It is in BCNF. - with FD
N → O. Key is . It is in BCNF. - Thus, statement (B) is TRUE.
- .
- Since is a candidate key for both and , the intersection is a key for at least one of the decomposed relations. This guarantees a lossless join. Thus, statement (C) is TRUE.
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