If relation with Schema is decomposed into two relations and
Duration: 1 min
2014
If a relation with a Schema R is decomposed into two relations R₁ and R₂ such that (R₁ ∪ R₂) = R₁ then which one of the following is to be satisfied for a lossless joint decomposition (→ indicates functional dependency)
- A.
(R₁ ∩ R₂) → R₁ or (R₁ ∩ R₂) → R₂
- B.
R₁ ∩ R₂ → R₁
- C.
R₁ ∩ R₂ → R₂
- D.
R₁ ∩ R₂ → R₁ and R₁ ∩ R₂ → R₂
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Correct answer: A
For a decomposition of relation R into relations R₁ and R₂ to be lossless, the intersection of their attributes must functionally determine at least one of the relations. This ensures that joining R₁ and R₂ back together reconstructs the original relation without generating spurious tuples. Therefore, the condition (R₁ ∩ R₂) → R₁ or (R₁ ∩ R₂) → R₂ must be satisfied.
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