Consider the relation R(A,B,C,D,E,F) with the following set of functional…
Consider the relation R(A,B,C,D,E,F) with the following set of functional dependencies: {A→B, C→D, E→F, AC→E}
The relation R is decomposed into three sub-relations: R1(A,B,C), R2(C,D,E), R3(A,C,E,F) then how many statements are correct?
S1: Lossless Decomposition
S2: Dependency preserving decomposition
Answer: 2 — S1: Lossless Decomposition Use common attribute superkey rule for checking pairwise: R1 ∩ R3 = {A, C} AC+ in R3 = AC → E, E → F ⇒ AC+ = {A, C, E, F} AC is a…
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Correct answer: 2
S1: Lossless Decomposition
Use common attribute superkey rule for checking pairwise:
R1 ∩ R3 = {A, C}
AC+ in R3 = AC → E, E → F ⇒ AC+ = {A, C, E, F}
AC is a superkey in R3
R2 ∩ R3 = {C, E}
CE+ in R2 = C → D, CE → nothing more ⇒ CE+ = {C, D, E}
CE is a superkey in R2
Lossless Decomposition is TRUE
S2: Dependency Preserving
Check if all FDs are preserved in individual relations:
A → B — present in R1
C → D — present in R2
E → F — present in R3
AC → E — present in R3
All FDs are preserved