In a schema with attributes A, B, C, D and E following set of functional dependencies are givenA → B A → C CD → E B → D E → AWhich of the following functional dependencies is NOT implied by the above set?*AC → BCCD → ACBC → CDBD → CD
Question
In a schema with attributes A, B, C, D and E following set of functional dependencies are givenA → B A → C CD → E B → D E → AWhich of the following functional dependencies is NOT implied by the above set?*AC → BCCD → ACBC → CDBD → CD
Solution
The functional dependency that is NOT implied by the given set is BD → CD.
Here's the step-by-step reasoning:
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A → B, A → C: These two dependencies imply that A → BC.
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CD → E: This dependency is given.
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B → D: This dependency is given.
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E → A: This dependency is given.
Now, let's check the options:
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AC → BC: This is implied because we know A → BC.
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CD → AC: This is implied because we know CD → E and E → A.
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BC → CD: This is implied because we know B → D.
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BD → CD: This is NOT implied by the given set. We know B → D, but we don't have any dependency that would allow us to infer D → C or BD → C. Therefore, this is the correct answer.
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