Let r be a relation instance with schema R = (A, B, C, D). Define r1 =…
2005
Let r be a relation instance with schema R = (A, B, C, D).
Define r1 = πA,B,C(r) and r2 = πA,D(r). Let S = r1 ⋈ r2, where ⋈ denotes natural join.
Given that the decomposition of R into r1 and r2 is lossy, which one of the following is true?
- A.
S ⊂ R
- B.
R ∪ S
- C.
R ⊂ S
- D.
R ⋈ S = S
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Correct answer: C
When a relation is projected into smaller relations and then joined back, the original tuples are always present in the join. So R is a subset of S.
A lossy decomposition means the join produces extra/spurious tuples. Therefore, S contains more tuples than R.
Hence the strict containment is R ⊂ S, not S ⊂ R.
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