Q18,paper 3,j 12. Consider a schema R(A, B, C, D) and functional dependencies A →B and C→D. Then the decomposition R1(A, B) and R2(C, D) is

Options.
(A) Dependency preserving but not lossless join
(B) Dependency preserving and lossless join
(C) Lossless Join but not dependency preserving
(D) Lossless Join.
Answer(A) Dependency preserving but not lossless join.
Explanation .When the decomposition is done R1(A, B) and R2(C, D) then dependencies A →B and C→D are preserved in R1 and R2. For lossless join it can be checked as
R1 intersection R2 -> R1
or
R1 intersection R2 -> R2.
As there is no common attribute of R1 and R2 hence common attribute cannot derives all the attributes of any relation. Hence it is lossy join.