Consider a relation R(A,B,C,D) with functional dependencies {A→B,B→C,C→D}. How…
Consider a relation R(A,B,C,D) with functional dependencies {A→B,B→C,C→D}. How many statements are correct if the decomposition of R will be R1(A,B), R2(B,C) and R3(C,D)
S1: Lossless Decomposition
S2: Dependency Preserving Decomposition
S3: 3NF
S4: BCNF
Answer: 4 — S1: Lossless Decomposition True – R1 and R2 share B (key in R2 because B→C), R2 and R3 share C (key in R3 because C→D) → So, lossless join is ensured by…
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Correct answer: 4
S1: Lossless Decomposition
True –
R1 and R2 share B (key in R2 because B→C),
R2 and R3 share C (key in R3 because C→D)
→ So, lossless join is ensured by common key attribute rule.
S2: Dependency Preserving
True – As there is not composite CK
All FDs (A→B, B→C, C→D) can be checked locally in R1, R2, R3.
S3: 3NF
True –
All FDs satisfy 3NF condition in their respective relations.
S4: BCNF
True –
In each sub-relation, LHS of FD is a super key ⇒ satisfies BCNF.