Which of the following statements is TRUE? D₁ : The decomposition of the schema R(A, B, C) into R₁(A, B) and R₂ (A, C) is always lossless. D₂ : The…
Which of the following statements is TRUE? D₁ : The decomposition of the schema R(A, B, C) into R₁(A, B) and R₂ (A, C) is always lossless. D₂ : The decomposition of the schema R(A, B, C, D, E) having AD →B, C →DE, B → AE and AE →C, into R₁ (A, B, D) and R₂ (A, C, D, E) is lossless.
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Correct answer: (D) Only D₂
Explanation
D₂: R₁ ∩ R₂ = {A, D}, and AD → B, so AD is a key of R₁ (A, B, D); the decomposition is lossless. D₁ is not always lossless since no FDs are given: if B → A and C → A, then the common attribute A is not a key of either table, so the decomposition is lossy. Hence only D₂.