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Let r_i(z) and w_i(z) denote read and write operations, respectively, on a data item z by a transaction T_i. Consider the following two schedules: S₁: r₁(x) r₁(y) r₂(x) r₂(y) w₂(y) w₁(x) S₂: r₁(x) r₂(x) r₂(y) w₂(y) r₁(y) w₁(x) Which one of the following options is correct?

1. D₁ is a lossless decomposition, but D₂ is a lossy decomposition.
2. D₁ is a lossy decomposition, but D₂ is a lossless decomposition.
3. Both D₁ and D₂ are lossless decompositions.
4. Both D₁ and D₂ are lossy decompositions.

Correct answer: Both D₁ and D₂ are lossy decompositions.

Solution

A decomposition is lossless only if the intersection of the decomposed relations functionally determines one of them. In the given case, the schedules correspond to decompositions that do not satisfy the lossless-join condition, so both are lossy.

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