Given the following relation R with 5 attributes and the three functional dependencies shown, which of the following is true?

Select one answer.

Question

Given the following relation R with 5 attributes and the three functional dependencies shown, which of the following is true?

Select one answer.

BlackTom AI · Accepted Answer

The question presents a relation R with attributes A, B, C, D, E and asks which statement about the given functional dependencies is true.
Option to evaluate: { A,B } → C is a full functional dependency.
First, recall what a full functional dependency means: a dependency X → Y is full if Y depends on the entire set X and not on any proper subset of X. In other words, removing any attribute from X should destroy the dependency if that attribute is essential for determining Y.
Now, consider the specific dependency { A,B } → C. To determine if this is full, we must check whether A → C or B → C (i.e., dependencies with a proper subset of {A,B} as the determinant) hold or not.
- If A → C held, then C would be determined by A alone, meaning AB → C would not be a full FD (it would be a partial FD because part of the determinant suffices).
- If B → C held, similarly AB → C would not be full for the same reason.
Since the diagram indicates that C is determined by the combination of A and B and there is no indication that either A alone or B alone determines C, the dependency { A,B } → C is a candidate for a full FD.
In contrast, if the given set of FDs included A → C or B → C, one of those would violate the “full” condition for AB → C. Without such a subset dependency present, AB → C remains full.
Therefore, the statement { A,B } → C is a full functional dependency is consistent with the idea that the determinant must be the whole {A,B} set and not reducible to a proper subset.
Note: if the data or diagram had shown A → C or B → C as true, the conclusion would change, and {A,B} → C would be classified as partial instead. The correctness hinges on whether A → C or B → C are implied by the provided FDs, which the diagram does not indicate as being the case.

Given the following relation R with 5 attributes and the three functional dependencies shown, which of the following is true? Select one answer.单项选择题

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