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Suppose that we have the following three tuples in a legal instance of a relation schema S with three attributes ABC (listed in order): (1,2,3), (4,2,3), and (5,3,3). Which of the following dependencies can you infer does not hold over schema S?
- a)A → B
- b)BC → A
- c)B → C
- d)BA → C
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Suppose that we have the following three tuples in a legal instance o...
BC→ A does not hold over S (look at the tuples (1,2,3) and (4,2,3)). The other tuples hold over S.
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Most Upvoted Answer
Suppose that we have the following three tuples in a legal instance o...
Explanation:
To determine which dependency does not hold over schema S, we need to check if each dependency holds for all tuples in the relation.
Given the tuples (1,2,3), (4,2,3), and (5,3,3), let's analyze each dependency:
a) A → B:
- A = {1, 4, 5} and B = {2, 2, 3}
- Since A uniquely determines B (each value in A corresponds to a unique value in B), the dependency A → B holds for all tuples.
b) BC → A:
- BC = {(2,3), (2,3), (3,3)}
- A = {2, 2, 3}
- In this case, BC does not uniquely determine A (the same combination of values in BC can correspond to different values in A).
- For example, (2,3) can correspond to A=2 or A=3.
- Therefore, the dependency BC → A does not hold for all tuples.
c) B → C:
- B = {2, 2, 3} and C = {3, 3, 3}
- Since B uniquely determines C (each value in B corresponds to a unique value in C), the dependency B → C holds for all tuples.
d) BA → C:
- BA = {(2,1), (2,4), (3,5)}
- C = {3, 3, 3}
- In this case, BA does not uniquely determine C (the same combination of values in BA can correspond to different values in C).
- For example, (2,4) can correspond to C=3 or C=5.
- Therefore, the dependency BA → C does not hold for all tuples.
Conclusion:
Based on the analysis above, the dependency that does not hold over schema S is BC → A (option B).
To determine which dependency does not hold over schema S, we need to check if each dependency holds for all tuples in the relation.
Given the tuples (1,2,3), (4,2,3), and (5,3,3), let's analyze each dependency:
a) A → B:
- A = {1, 4, 5} and B = {2, 2, 3}
- Since A uniquely determines B (each value in A corresponds to a unique value in B), the dependency A → B holds for all tuples.
b) BC → A:
- BC = {(2,3), (2,3), (3,3)}
- A = {2, 2, 3}
- In this case, BC does not uniquely determine A (the same combination of values in BC can correspond to different values in A).
- For example, (2,3) can correspond to A=2 or A=3.
- Therefore, the dependency BC → A does not hold for all tuples.
c) B → C:
- B = {2, 2, 3} and C = {3, 3, 3}
- Since B uniquely determines C (each value in B corresponds to a unique value in C), the dependency B → C holds for all tuples.
d) BA → C:
- BA = {(2,1), (2,4), (3,5)}
- C = {3, 3, 3}
- In this case, BA does not uniquely determine C (the same combination of values in BA can correspond to different values in C).
- For example, (2,4) can correspond to C=3 or C=5.
- Therefore, the dependency BA → C does not hold for all tuples.
Conclusion:
Based on the analysis above, the dependency that does not hold over schema S is BC → A (option B).
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Suppose that we have the following three tuples in a legal instance of a relation schema S with three attributes ABC (listed in order): (1,2,3), (4,2,3), and (5,3,3). Which of the following dependencies can you infer does not hold over schema S?a)A → Bb)BC → Ac)B → Cd)BA → CCorrect answer is option 'B'. Can you explain this answer?
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