Consider a schema R(P, Q, R, S) and the functional dependencies P → Q, Q → R, R → S, S → Q. Then the decomposition of R into R₁(P, Q), R₂(Q, R) and R₃(Q, S) is:
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Correct answer: A. Dependency preserving and lossless join
Explanation
Q, R and S determine one another (Q → R → S → Q). P → Q holds in R₁, Q → R in R₂ and Q ↔ S in R₃, and R → S follows from R → Q (in R₂) and Q → S (in R₃), so all FDs are preserved. Joining R₁ and R₂ on Q (Q is a key of R₂) and then R₃ on Q (Q → S) is lossless.More Database Management Systems questions
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