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Consider relation R(A,B,C,D,E) with functional dependencies:D -> C, CE -> A, D -> A, AE -> DWhich of the following is a key?CDEABCECE

Question

Consider relation R(A,B,C,D,E) with functional dependencies:D -> C, CE -> A, D -> A, AE -> DWhich of the following is a key?CDEABCECE

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Solution

To determine which of the following is a key for the relation R(A,B,C,D,E) with the given functional dependencies, we need to find a minimal set of attributes that can determine all other attributes in the relation.

The functional dependencies are: D -> C, CE -> A, D -> A, AE -> D

Let's analyze each proposed key:

  1. CDE: Using the functional dependencies, we can derive A from CE (CE -> A) and B is not dependent on any other attribute, so it cannot be derived. Therefore, CDE is not a key.

  2. ABCE: Using the functional dependencies, we can derive D from AE (AE -> D) and all other attributes are already included. Therefore, ABCE is a key.

  3. CE: Using the functional dependencies, we can derive A from CE (CE -> A) and D from AE (AE -> D), but B is not dependent on any other attribute, so it cannot be derived. Therefore, CE is not a key.

So, the only key from the given options is ABCE.

This problem has been solved

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