Consider the relation π(π,π, π , π, π,π) with the following set ofβ¦
2015
Consider the relation π(π,π, π , π, π,π) with the following set of functional dependencies
πΉ = {
Β Β Β Β Β Β Β Β {π, π } β {π, π},
Β Β Β Β Β Β Β Β {π, π,π} β {π, π }
}
Which of the following is the trivial functional dependency in πΉ+, where πΉ+ is closure of F ?
- A.
{π, π } β {π, π}
- B.
{π, π } β {π , π}
- C.
{π, π} β {π}
- D.
{π, π,π} β {π}
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Correct answer: C
Answer: {π, π} β {π} is the trivial functional dependency.
Reason: a functional dependency is trivial when every attribute on the right-hand side also appears on the left-hand side.
Here, π appears on both sides of {π, π} β {π}, so it is trivial and therefore belongs to F+ without using the other dependencies.
Other choices either require deriving attributes from the given FDs (so they are non-trivial) or include right-hand attributes not present in the left-hand side, so they are not trivial.
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