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Consider the following statements given below:
S1: There is always a lossless, dependency preserving BCNF decomposition.
S2: Any relation with two attributes is in BCNF.
S3: For two relations R(A, B) and functional dependency F = {A → B} and S(B, C) and functional dependency F = {B → C}, natural join is in BCNF.
Which of the following statements are true?
- a)S1 and S2 only
- b)S2 and S3 only
- c)S1, S2 and S3
- d)None of the above
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Consider the following statements given below:S1: There is always a l...
S1 : Lossless dependency preserving BCNF decomposition is not always possible. S1 false
S2 : With two attributes a relation is always in. BCNF. S2 true
R(A, B)
A → B, B → A
Both A and B are key for R.
S3 : The natural join of R and S will have functional dependencies A → B and B → C, which is not in BCNF. S3 false
So option (D) is correct.
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Community Answer
Consider the following statements given below:S1: There is always a l...
Analysis of Statements
To understand the correctness of the statements, let's analyze each one.
S1: There is always a lossless, dependency preserving BCNF decomposition.
- Explanation: This statement is incorrect. While BCNF decomposition can be performed, it is not guaranteed to be both lossless and dependency preserving simultaneously. In many cases, when decomposing a relation into BCNF, some functional dependencies may be lost, which can lead to difficulties in reconstructing the original relation.
S2: Any relation with two attributes is in BCNF.
- Explanation: This statement is true. A relation with two attributes (A, B) can only have functional dependencies involving these two attributes. The possible dependencies are A → B or B → A. In both scenarios, the relation satisfies the BCNF conditions as every determinant is a superkey.
S3: For two relations R(A, B) and functional dependency F = {A → B} and S(B, C) and functional dependency F = {B → C}, natural join is in BCNF.
- Explanation: This statement is false. A natural join of R and S results in a relation with attributes A, B, and C. The functional dependency A → C may exist due to the dependencies A → B and B → C. This means that the resulting relation may violate BCNF if A is not a superkey.
Conclusion
Based on the analyses:
- S1 is false.
- S2 is true.
- S3 is false.
Thus, the correct answer is option D: None of the above.
To understand the correctness of the statements, let's analyze each one.
S1: There is always a lossless, dependency preserving BCNF decomposition.
- Explanation: This statement is incorrect. While BCNF decomposition can be performed, it is not guaranteed to be both lossless and dependency preserving simultaneously. In many cases, when decomposing a relation into BCNF, some functional dependencies may be lost, which can lead to difficulties in reconstructing the original relation.
S2: Any relation with two attributes is in BCNF.
- Explanation: This statement is true. A relation with two attributes (A, B) can only have functional dependencies involving these two attributes. The possible dependencies are A → B or B → A. In both scenarios, the relation satisfies the BCNF conditions as every determinant is a superkey.
S3: For two relations R(A, B) and functional dependency F = {A → B} and S(B, C) and functional dependency F = {B → C}, natural join is in BCNF.
- Explanation: This statement is false. A natural join of R and S results in a relation with attributes A, B, and C. The functional dependency A → C may exist due to the dependencies A → B and B → C. This means that the resulting relation may violate BCNF if A is not a superkey.
Conclusion
Based on the analyses:
- S1 is false.
- S2 is true.
- S3 is false.
Thus, the correct answer is option D: None of the above.
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Consider the following statements given below:S1: There is always a lossless, dependency preserving BCNF decomposition.S2: Any relation with two attributes is in BCNF.S3: For two relations R(A, B) and functional dependency F = {A → B} and S(B, C) and functional dependency F = {B → C}, natural join is in BCNF.Which of the following statements are true?a)S1 and S2 onlyb)S2 and S3 onlyc)S1, S2 and S3d)None of the aboveCorrect answer is option 'D'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the following statements given below:S1: There is always a lossless, dependency preserving BCNF decomposition.S2: Any relation with two attributes is in BCNF.S3: For two relations R(A, B) and functional dependency F = {A → B} and S(B, C) and functional dependency F = {B → C}, natural join is in BCNF.Which of the following statements are true?a)S1 and S2 onlyb)S2 and S3 onlyc)S1, S2 and S3d)None of the aboveCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements given below:S1: There is always a lossless, dependency preserving BCNF decomposition.S2: Any relation with two attributes is in BCNF.S3: For two relations R(A, B) and functional dependency F = {A → B} and S(B, C) and functional dependency F = {B → C}, natural join is in BCNF.Which of the following statements are true?a)S1 and S2 onlyb)S2 and S3 onlyc)S1, S2 and S3d)None of the aboveCorrect answer is option 'D'. Can you explain this answer?.
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