Gate2019 cs Q42

42Let 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 Y 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 lossless
Which of the above statements is/are correct?

Option : C
Explanation :
X(PQRS) {QR → S, R → P, S → Q} decomposed into
Y(PR) Z(QRS)
{R → P} {QR → S, S → Q}
Candidate key : R Candidate key : QR, RS
Relation Y in BCNF Relation Z in 3NF but not BCNF
The common attribute between Y and Z relations is R which is key for relation Y.
So that given decomposition is lossless join decomposition.
R → P in Y

and dependency preserving decomposition.
Hence, C is the correct answer.

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