Consider a schema $R(A,B,C,D)$ and functional dependencies $A \rightarrow B$ and $C \rightarrow D$. Then the decomposition of R into $R_1 (A,B)$ and $R_2(C,D)$ is
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Detailed Video Solution
Answer is C. Here, no common attribute in R1 and R2, therefore lossy join will be there. and both the dependencies are preserved in composed relations so, dependency preserving.
Its 1NF .
Candidate key = {AC}
Not 2NF because both dependencies have partial dependency.
eg : In A-->B , A is proper subset of Candidate key and B is a non-prime attribute.
@Arjun sir
The answer key is wrong in GO pdf for this question. kindly check once!
A decomposition {R1, R2} is a lossless-join decomposition if R1 ∩ R2 → R1 (R1 should be key) or R1 ∩ R2 → R2 (R2 should be key) but (A,B) ∩ (C,D) = ∅ so lossy join
FD:1 A→B
FD:2 C→D
R1(A,B) have all attributes of FD1 and R2(C,D) have all attributes of FD2 so ,dependency preserved decompostion
Reference : - question no. 8.1 Korth http://codex.cs.yale.edu/avi/db-book/db6/practice-exer-dir/8s.pdf
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