Question

Let R(A,B,C,D,E) be a relation with FDs F = {AB-CD, A-E, C-D, D-E} The decomposition of Rinto R1(A, B, C), R2(B, C, D) and R3(C, D, E) is 2 Points) Select one: Lossless and Dependency Preserving. Lossy and Not Dependency Preserving. Lossless and Not Dependency Preserving. Lossy and Dependency Preserving.

Answer 1

Correct Answer :

Lossy and Not Dependency Preserving

Reason :

• FDs = { AB ->CD ,A ->E , C ->D , D->E}
• Now , based on this dependies , the minimal cover will be :

1. A,B --> C
2. A --> E
3. C --> D
4. D --> E

• From this , on the RHS , only A,B is not missing .
• Now , taking {A,B}⁺ = {A,B,C,D,E} => AB is candidate key
• Now , relation R1(A,B,C) , FD set is AB->C.
• Now , relation R2(B,C,D) , FD set is C->D.
• Now , relation R3(C,D,E) , FD set is C->D,D->E.
• Here, A->E cannot be derived, hence the decomposition is not dependency preserving.
• Here, the common attribute in R1 and R2 is C, which is not the Candidate key in either of the relation, hence decomposition is not lossless.