Consider a schema R(P, Q, R, S) and the following functional dependencies P→Q, Q→R, R→S, S→Q. Then decomposition of R1(P, Q), R2(Q, R) and R3(Q, S) is:

Correct option is A

For a decomposition to be dependency-preserving and lossless join:
1. Dependency Preservation means that each functional dependency is represented in at least one of the decomposed relations.
2. Lossless Join ensures that no information is lost when the decomposed relations are joined back.
Given functional dependencies:
· P → Q, Q → R, R → S, S → Q
Decomposed relations:
· R1(P, Q), R2(Q, R) and R3(Q, S)
Information Booster
· Since each functional dependency is represented in at least one of the decomposed relations, the decomposition is dependency-preserving.
· Joining R1, R2 and R3 will give back the original relation without any loss, making it lossless join.
Additional Knowledge
Option (b): Incorrect because it implies loss of dependency preservation.
Option (c) and (d): Incorrect due to incorrect assumptions about dependency preservation and lossless join.