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: 2S1: 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:

  1. A → B — present in R1 

  2. C → D — present in R2 

  3. E → F — present in R3 

  4. AC → E — present in R3 

All FDs are preserved

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