Last Updated :
30 Oct, 2018
Consider the statements about decomposition of a relation R is decomposed into R1, R2, R3, R4, …. Rn with functional dependencies F1, F2, F3, …, Fn of functional dependency F. Which of the following option is correct regarding conditions of adequate decomposition? (Assume R1∪R2∪R3∪ …. Rn ≡ R).
(A) R1⋈R2⋈R3⋈ …. Rn ≡ R, and F1∪F2∪F3∪ …∪ Fn ⊂ F respectively
(B) R1⋈R2⋈R3⋈ …. Rn ⊃ R and F1∪F2∪F3∪ …∪Fn ≡ F respectively
(C) R1⋈R2⋈R3⋈ …. Rn ≡ R and F1∪F2∪F3∪ …∪Fn ⊃ F respectively
(D) None of the above
Answer: (D)
Explanation:
- R1⋈R2⋈R3⋈……Rn ≡ R is lossless join
- R1⋈R2⋈R3⋈……Rn ⊂ R is lossy join
- R1⋈R2⋈R3⋈……Rn ⊃ R is not possible
- F1∪F2∪F3∪ …∪Fn ≡ F is preserving dependency
- F1∪F2∪F3∪ …∪Fn ⊂ F is not preserving dependency
- F1∪F2∪F3∪ …∪Fn ⊃ F is not possible
For adequate decomposition, decomposition should be lossless join and dependency preserving.
So, option (D) is correct.
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