Functional dependencies: implicationWe have the attributes: {A, B, C, D, E, F, G}.Consider the following functional dependenciesA, D, F -> EE, F, G -> DA, B -> FE -> BC, G -> D, FC, G -> B, EA, C -> EA -> C, EMark all functional dependencies that are implied by the dependencies above:A, C -> EA, C -> BA, C -> B, DA, C -> CA, C -> C, F
Question
Functional dependencies: implicationWe have the attributes: {A, B, C, D, E, F, G}.Consider the following functional dependenciesA, D, F -> EE, F, G -> DA, B -> FE -> BC, G -> D, FC, G -> B, EA, C -> EA -> C, EMark all functional dependencies that are implied by the dependencies above:A, C -> EA, C -> BA, C -> B, DA, C -> CA, C -> C, F
Solution
To determine the implied functional dependencies, we need to use the concept of closure. The closure of a set of attributes X under a set of functional dependencies F, denoted as X+, is the set of attributes that are functionally determined by X under F.
Let's go through each of the proposed functional dependencies:
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A, C -> E: This is not implied. The given dependencies do not allow us to derive E from A and C.
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A, C -> B: This is not implied. The given dependencies do not allow us to derive B from A and C.
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A, C -> B, D: This is not implied. The given dependencies do not allow us to derive B and D from A and C.
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A, C -> C: This is implied. Any set of attributes trivially functionally determines itself.
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A, C -> C, F: This is not implied. The given dependencies do not allow us to derive C and F from A and C.
So, the only functional dependency that is implied by the given dependencies is A, C -> C.
Similar Questions
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correct answerWe can use the following three rules to find logically implied functional dependencies. This collection of rules is called
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