Let r be a rational instance with schema R = (A, B, C, D).

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Let r be a rational instance with schema R = (A, B, C, D). We define r₁ = Π_{A, B, C}(r) and r₂ = Π_{A, 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?

1. s ⊂ r
2. r ∪ s = r
3. r ⊂ s
4. r * s = s

Correct Option: C

R = (A, B, C, D)
r₁ = Π_{A , B , C} (R) and r₂ = Π_{A , D} (r)
s = r₁ * r₂
The tuples in s are more than that of r. Also, s consists of all the tuples of r along with other tuples. Therefore, the most appropriate relation is r ⊂ s .