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

1)
B ---> C, D ---> A
i. Candidate keys: BD
ii. Both B ---> C and D ---> A cause BCNF violations.
As per proposed it into BC and AD violates the BCNF rules. Because there is no relation between them.One possible decomposition is AD, BC, BD is BCNF and it is lossless.

2)
AB -> C, C -> A, C -> D
i. Candidate keys: AB,CB
ii. As per proposed it into ACD and BC gives good decomposition as per BCNF rules. In BC, C acts as primary keya nd in ACD, C acts as foreign key so that relation exists.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.