Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Consider a schema R(A,B,C,D) and functional d...
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Consider a schema R(A,B,C,D) and functional dependencies A->B and C->D. Then the decomposition of R into R1(AB) and R2(CD) is
- a)dependency preserving and lossless join
- b)lossless join but not dependency preserving
- c)dependency preserving but not lossless join
- d)not dependency preserving and not lossless join
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Consider a schema R(A,B,C,D) and functional dependencies A->B and ...
Dependency Preserving Decomposition:
Decomposition of R into R1 and R2 is a dependency preserving decomposition if closure of functional dependencies after decomposition is same as closure of of FDs before decomposition.
A simple way is to just check whether we can derive all the original FDs from the FDs present after decomposition.
Decomposition of R into R1 and R2 is a dependency preserving decomposition if closure of functional dependencies after decomposition is same as closure of of FDs before decomposition.
A simple way is to just check whether we can derive all the original FDs from the FDs present after decomposition.
In the above question R(A, B, C, D) is decomposed into R1 (A, B) and R2(C, D) and there are only two FDs A -> B and C -> D. So, the decomposition is dependency preserving
Lossless-Join Decomposition:
Decomposition of R into R1 and R2 is a lossless-join decomposition if at least one of the following functional dependencies are in F+ (Closure of functional dependencies)
Decomposition of R into R1 and R2 is a lossless-join decomposition if at least one of the following functional dependencies are in F+ (Closure of functional dependencies)
R1 ∩ R2 → R1
OR
R1 ∩ R2 → R2
OR
R1 ∩ R2 → R2
In the above question R(A, B, C, D) is decomposed into R1 (A, B) and R2(C, D), and R1 ∩ R2 is empty. So, the decomposition is not lossless.
Most Upvoted Answer
Consider a schema R(A,B,C,D) and functional dependencies A->B and ...
Explanation:
To decompose the schema R(A,B,C,D) into R1(AB) and R2(CD), we need to check if the decomposition is dependency preserving and lossless join.
Dependency Preservation:
A decomposition is said to preserve dependencies if every functional dependency in the original schema is also present in at least one of the decomposed schemas. In this case, the functional dependencies are A-B and C-D. Let's check if these dependencies hold in the decomposed schemas:
- R1(AB) has the attribute A and B, and A-B dependency holds in it.
- R2(CD) has the attribute C and D, and C-D dependency holds in it.
Therefore, the decomposition is dependency preserving.
Lossless Join:
A decomposition is said to be lossless join if we can join the decomposed schemas to get the original schema without losing any information. In this case, we need to check if the natural join of R1 and R2 gives us the original schema R.
The natural join of R1(AB) and R2(CD) will give us a schema with attributes ABCD. Since R has attributes ABCD, the decomposition is lossless join.
Conclusion:
Since the decomposition is both dependency preserving and lossless join, the correct answer is option 'C' - dependency preserving but not lossless join.
To decompose the schema R(A,B,C,D) into R1(AB) and R2(CD), we need to check if the decomposition is dependency preserving and lossless join.
Dependency Preservation:
A decomposition is said to preserve dependencies if every functional dependency in the original schema is also present in at least one of the decomposed schemas. In this case, the functional dependencies are A-B and C-D. Let's check if these dependencies hold in the decomposed schemas:
- R1(AB) has the attribute A and B, and A-B dependency holds in it.
- R2(CD) has the attribute C and D, and C-D dependency holds in it.
Therefore, the decomposition is dependency preserving.
Lossless Join:
A decomposition is said to be lossless join if we can join the decomposed schemas to get the original schema without losing any information. In this case, we need to check if the natural join of R1 and R2 gives us the original schema R.
The natural join of R1(AB) and R2(CD) will give us a schema with attributes ABCD. Since R has attributes ABCD, the decomposition is lossless join.
Conclusion:
Since the decomposition is both dependency preserving and lossless join, the correct answer is option 'C' - dependency preserving but not lossless join.
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Consider a schema R(A,B,C,D) and functional dependencies A->B and ...
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Consider a schema R(A,B,C,D) and functional dependencies A->B and C->D. Then the decomposition of R into R1(AB) and R2(CD) isa)dependency preserving and lossless joinb)lossless join but not dependency preservingc)dependency preserving but not lossless joind)not dependency preserving and not lossless joinCorrect answer is option 'C'. Can you explain this answer?
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