Let the set of functional dependencies F = {QR → S, R → P, S → Q} hold on a relation schema X = (PQRS). X is not in BCNF. Suppose X is decomposed into two schemas and Z where Y = (PR) and Z = (QRS). Consider the two statements given below:
- I. Both Y and Z are in BCNF
- II. Decomposition of X into Y and Z is dependency preserving and a lossless.
Which of the above statements is/are correct?
(A) I only
(B) Neither I nor II
(C) Both I and II
(D) II only
Answer: (D)
Explanation: X(PQRS) {QR → S, R → P, S → Q} decomposed into Y (PR) and Z (QRS). So,
| Y (PR) | Z (QRS) |
|---|---|
| {R → P} Candidate key : {R} So, relation Y in BCNF | {QR → S, S → Q} Candidate key : {QR, RS} So, relation Z in 3NF but not BCNF, becasuse of S is not superkey. |
Since, this decomposition covers all functional dependencies of original relation (X), so decomposition of X into Y and Z is dependency preserving.
Also, this decomposition has common attribute (i.e., R) which is superkey of relation Y(PR), so so decomposition of X into Y and Z is also lossless join decomposition.
Option (D) is correct.
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