Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Find the minimal set of FDs.R(A, B, C, D)F : ...
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Find the minimal set of FDs.
R(A, B, C, D)
F : { A -> B, C -> B, D -> ABC, AC -> D}
R(A, B, C, D)
F : { A -> B, C -> B, D -> ABC, AC -> D}
- a)F : { A -> B, C -> B, D -> AB, AC -> D}
- b)F : { A -> B, C -> B, D -> AC, AC -> D}
- c)F : { A -> B, C -> B, D -> BC, AC -> D}
- d)None
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Find the minimal set of FDs.R(A, B, C, D)F : { A -> B, C -> B, D...
Understanding Functional Dependencies (FDs)
To find the minimal set of functional dependencies (FDs), we need to analyze the given set and identify redundancies or dependencies that can be derived from others.
Given Functional Dependencies
The original set of FDs is:
- A -> B
- C -> B
- D -> ABC
- AC -> D
Analyzing Each Option
1. Option a: { A -> B, C -> B, D -> AB, AC -> D }
- D -> ABC is stronger than D -> AB. This means D -> AB is redundant since D -> ABC can imply D -> AB.
2. Option b: { A -> B, C -> B, D -> AC, AC -> D }
- D -> AC is a valid dependency. AC -> D suggests a bidirectional relationship, making it minimal.
3. Option c: { A -> B, C -> B, D -> BC, AC -> D }
- D -> ABC is stronger than D -> BC. Thus, D -> BC is redundant.
4. Option d: None
- Indicates that all previous options are not minimal. However, option b is minimal.
Why Option B is Correct
- Minimality: In option b, all FDs are necessary; removing any one leads to loss of information or the ability to derive other attributes.
- Coverage: D -> AC ensures that we can retrieve attributes A and C from D, while AC -> D maintains the dependency on D.
Conclusion
The correct answer is option b, as it provides a minimal and non-redundant set of functional dependencies while covering all necessary relationships between the attributes A, B, C, and D.
To find the minimal set of functional dependencies (FDs), we need to analyze the given set and identify redundancies or dependencies that can be derived from others.
Given Functional Dependencies
The original set of FDs is:
- A -> B
- C -> B
- D -> ABC
- AC -> D
Analyzing Each Option
1. Option a: { A -> B, C -> B, D -> AB, AC -> D }
- D -> ABC is stronger than D -> AB. This means D -> AB is redundant since D -> ABC can imply D -> AB.
2. Option b: { A -> B, C -> B, D -> AC, AC -> D }
- D -> AC is a valid dependency. AC -> D suggests a bidirectional relationship, making it minimal.
3. Option c: { A -> B, C -> B, D -> BC, AC -> D }
- D -> ABC is stronger than D -> BC. Thus, D -> BC is redundant.
4. Option d: None
- Indicates that all previous options are not minimal. However, option b is minimal.
Why Option B is Correct
- Minimality: In option b, all FDs are necessary; removing any one leads to loss of information or the ability to derive other attributes.
- Coverage: D -> AC ensures that we can retrieve attributes A and C from D, while AC -> D maintains the dependency on D.
Conclusion
The correct answer is option b, as it provides a minimal and non-redundant set of functional dependencies while covering all necessary relationships between the attributes A, B, C, and D.
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Community Answer
Find the minimal set of FDs.R(A, B, C, D)F : { A -> B, C -> B, D...
C → B
A → B
AC → D
D → ABC
Given that, D → ABC
A → B
AC → D
D → ABC
Given that, D → ABC
Case I:
B functionally dependent on A so we replace
B to A
D → AAC
D → AC
B functionally dependent on A so we replace
B to A
D → AAC
D → AC
Case II:
B functionally dependent on C, so we replace
B to C
D → ACC
D → AC
B functionally dependent on C, so we replace
B to C
D → ACC
D → AC
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