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Consider the following set of functional dependencies F on the schema S(P, Q, R)
F = {P → QR, PQ → R, Q → R, P → Q}
The canonical cover of the above given set is
F = {P → QR, PQ → R, Q → R, P → Q}
The canonical cover of the above given set is
- a)P → QR and PQ → R
- b)P → QR and P → Q
- c)P → Q and Q → R
- d)P → QR and Q → R
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Consider the following set of functional dependencies F on the schema ...
→ Q, Q → R}
This set of functional dependencies implies that:
- For any two tuples in the relation, if they have the same value for P, then they must also have the same value for Q (since P → Q).
- For any two tuples in the relation, if they have the same value for Q, then they must also have the same value for R (since Q → R).
We can use these functional dependencies to check for redundancies and anomalies in the relation. For example:
- Redundancy: If we have a tuple with values (1, 2, 3) and another tuple with values (1, 2, 4), we can see that the value of Q (2) is repeated unnecessarily. We could instead have a single tuple with values (1, 2, 3, 4). This is known as a functional dependency preservation, and we can use it to normalize the relation.
- Anomaly: If we have a tuple with values (1, 2, NULL) and another tuple with values (1, NULL, 4), we cannot determine the value of R for the tuple (1, 2, 4). This is known as a functional dependency violation, and we need to ensure that such anomalies do not occur in the relation. This can be achieved by enforcing constraints on the values allowed in the relation.
This set of functional dependencies implies that:
- For any two tuples in the relation, if they have the same value for P, then they must also have the same value for Q (since P → Q).
- For any two tuples in the relation, if they have the same value for Q, then they must also have the same value for R (since Q → R).
We can use these functional dependencies to check for redundancies and anomalies in the relation. For example:
- Redundancy: If we have a tuple with values (1, 2, 3) and another tuple with values (1, 2, 4), we can see that the value of Q (2) is repeated unnecessarily. We could instead have a single tuple with values (1, 2, 3, 4). This is known as a functional dependency preservation, and we can use it to normalize the relation.
- Anomaly: If we have a tuple with values (1, 2, NULL) and another tuple with values (1, NULL, 4), we cannot determine the value of R for the tuple (1, 2, 4). This is known as a functional dependency violation, and we need to ensure that such anomalies do not occur in the relation. This can be achieved by enforcing constraints on the values allowed in the relation.
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Community Answer
Consider the following set of functional dependencies F on the schema ...
Option 3: P → Q and Q → R
P+ = {P, Q, R}
It covers, P → QR, PQ → R and P → Q
Also, Q → R
It is also minimal
Therefore, P → Q and Q → R is the canonical cover of the above given set.
P+ = {P, Q, R}
It covers, P → QR, PQ → R and P → Q
Also, Q → R
It is also minimal
Therefore, P → Q and Q → R is the canonical cover of the above given set.
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Consider the following set of functional dependencies F on the schema S(P, Q, R)F = {P → QR, PQ → R, Q → R, P → Q}The canonical cover of the above given set isa)P → QR and PQ → Rb)P → QR and P → Qc)P → Q and Q → Rd)P → QR and Q → RCorrect answer is option 'C'. Can you explain this answer?
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