GATE CS 2014 Set 1 — Question 40
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Databases → Normalization → 1NF, 2NF, 3NF
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Question
Given the following two statements:S1: Every table with two single-valued attributes is in 1NF, 2NF, 3NF and BCNF.
S2: is a minimal cover for the set of functional dependencies .Which one of the following is CORRECT?
S2: is a minimal cover for the set of functional dependencies .Which one of the following is CORRECT?
Correct answer
(A) S1 is TRUE and S2 is FALSE.
Solution
S1: A relation with only two attributes
Proposed minimal cover .
For to be a cover of , the closure of attributes under must imply all FDs in . Specifically, check
Using : . This does not contain . Thus,
Thus, S2 is FALSE.
R(A, B) is always in BCNF. - If there are no non-trivial FDs, the key is , and it is in BCNF.
- If
A → B, then is the key. Since the LHS () is a superkey, it is in BCNF. - If
B → A, then is the key. Since the LHS () is a superkey, it is in BCNF. - If
A → BandB → A, both are keys. Both dependencies satisfy BCNF.
Proposed minimal cover .
For to be a cover of , the closure of attributes under must imply all FDs in . Specifically, check
AB → E in .Using : . This does not contain . Thus,
AB → E cannot be derived from . Therefore, is not equivalent to .Thus, S2 is FALSE.
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