Suppose you are given a relation scheme R = {A, B, C, D}. For each of the follow

Question

Suppose you are given a relation scheme R = {A, B, C, D}. For each of the following sets of functional dependencies, assuming those are the only dependencies that hold for R, do the following: i. Identify the candidate key(s) for R. ii. State whether or not the proposed decomposition of R into smaller relations is a good decomposition, briefly explaining why or why not. 1. {B -> C, D -> A}: decompose into BC and AD. 2. {AB -> C, C -> A, C -> D}: decompose into ACD and BC. 3. {A -> BC, C -> AD}: decompose into ABC and AD. 4. {A -> B, B -> C, C -> D}: decompose into AB and ACD. 5. {A -> B, B -> C, C -> D}: decompose into AB, AD and CD.

Explanation / Answer

Solution:

1)

The candidate keys are,

BD

dependency is not preserved in the second one

2)

Candidate key

AB, CB

it is a good decomposition because the dependency is presereved.

3)

Candidate keys

A, C

the decomposition is a bad decomposition because the decomposition is not preserved C willl not be a candidate key here.

4.

A is the candidate key

the decomosition is a bad decompostion

5.

A is the candidate key here

The dependency is preserved here so it is a good decomposition.

I hope this helps, please let me know in case of any doubt. Thumbs up if this helped.

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