Consider the following Relation R(ABCDEFH) and following dependencies set {A → B, AB → CD, C → E , D → F}. The given relation is decomposed into R₁(ABC) and R₂ (ADEF)
(A) Lossless join and dependency preserving decomposition.
(B) Not lossless join but dependency preserving decomposition
(C) Lossless join but not dependency preserving decomposition
(D) Not lossless join and not dependency preserving decomposition


Answer: (C)

Explanation: For checking lossless join:
I – R₁ ∪ R₂ = R
R₁(ABC) ∪ R₂ (ADEF) = R(ABCDEF)
II – R₁ ∩ R₂ = [SK] for R₁ or R₂
= [A]⁺ = ABCDEF
Now dependency preserving will be checked:
In R₁(ABC)
[A]⁺ = ABC
In R₂(ADEF)
[A]⁺ = NULL
[D]⁺ = F
[E]⁺ = NULL
[F]⁺ = NULL
Because of decomposition AB → D, C → E, is lost.
So, it is not the dependency preserving decomposition.
So, option (C) is correct.

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