Consider a schema R(A, B, C, D) and functional dependencies

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Consider a schema R(A, B, C, D) and functional dependencies A → B and C → D. Then the decomposition of R into R1 (AB) and R2 (CD) is

1. dependency preserving and lossless join
2. lossless join but not dependency preserving
3. dependency preserving but not lossless join
4. not dependency preserving and not lossless join

Correct Option: C

We need to check two paramenters for the solutions
1. Loseless join
2. Dependency preserving
1. Lossless join R₁ (AB) ∧ R₂ (CD) → R₁ (AB)
Also, R₁ (AB) ∧ R₂ (CD) → R₁ (CD)
But we know that
Functional dependencies A → B and C → D
Hence, the statement above is not possible. → R(ABCD) is not a lossless join.
2. Dependency preserving
Since, R₁ (AB) ∨ R₂ (CD) → R(ABCD) It is dependency preserving.