Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Assume that AB → C, C → D and D &ra...
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Assume that AB → C, C → D and D → A are simultaneously satisfied by a relation r(R). What are the candidate keys of this relation?
- a)AB, CD and AD
- b)AB and CD
- c)AB and DB
- d)ABCD and BC
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Assume that AB → C, C → D and D → A are simultaneously ...
Understanding Functional Dependencies
In the given relation r(R), we have the functional dependencies:
- AB → C
- C → D
- D → A
These dependencies dictate how the attributes relate to one another.
Finding Candidate Keys
A candidate key is a minimal set of attributes that can uniquely determine all other attributes in a relation. We can analyze the given functional dependencies to identify potential candidate keys.
Analyzing the Dependencies
1. Starting with AB:
- AB → C (can determine C)
- C → D (from C, we can derive D)
- D → A (from D, we can derive A)
- Thus, AB can determine A, B, C, and D.
2. Now, considering CD:
- CD does not determine A or B directly, so it can't be a candidate key.
3. Next, examining DB:
- D → A (can derive A)
- B remains undetermined, so DB cannot be a candidate key.
4. Finally, check ABCD:
- ABCD includes all attributes but is not minimal.
Conclusion: Valid Candidate Keys
The only minimal set that uniquely determines all attributes is AB.
However, we also find that DB can serve as a candidate key. This is because:
- From D, we can determine A.
- B is included, providing the necessary uniqueness.
Thus, the candidate keys are AB and DB.
Final Answer
The correct option is C) AB and DB.
In the given relation r(R), we have the functional dependencies:
- AB → C
- C → D
- D → A
These dependencies dictate how the attributes relate to one another.
Finding Candidate Keys
A candidate key is a minimal set of attributes that can uniquely determine all other attributes in a relation. We can analyze the given functional dependencies to identify potential candidate keys.
Analyzing the Dependencies
1. Starting with AB:
- AB → C (can determine C)
- C → D (from C, we can derive D)
- D → A (from D, we can derive A)
- Thus, AB can determine A, B, C, and D.
2. Now, considering CD:
- CD does not determine A or B directly, so it can't be a candidate key.
3. Next, examining DB:
- D → A (can derive A)
- B remains undetermined, so DB cannot be a candidate key.
4. Finally, check ABCD:
- ABCD includes all attributes but is not minimal.
Conclusion: Valid Candidate Keys
The only minimal set that uniquely determines all attributes is AB.
However, we also find that DB can serve as a candidate key. This is because:
- From D, we can determine A.
- B is included, providing the necessary uniqueness.
Thus, the candidate keys are AB and DB.
Final Answer
The correct option is C) AB and DB.
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Community Answer
Assume that AB → C, C → D and D → A are simultaneously ...
If closure defined the complete relation then become the candidate key.
- Closure of AB = (AB)+ = {A,B,C,D} //candidate key
- Closure of BC = (BC)+ = {A,B,C,D} //candidate key
- Closure of CD = (CD)+ = {C,D,A}
- Closure of DB = (DB)+= {B,C,D,A} //candidate key
- Closure of ABCD = (ABCD)+= {A,B,C,D} //super key
- Closure of AD = (AD)+ = {A,B,D}
The candidate keys are AB. BC, BD
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Assume that AB → C, C → D and D → A are simultaneously satisfied by a relation r(R). What are the candidate keys of this relation?a)AB, CD and ADb)AB and CDc)AB and DBd)ABCD and BCCorrect answer is option 'C'. Can you explain this answer?
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