GATE Computer Science (CS) 2019 Solved Papers

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
Common attribute between Y and Zrelations is R which is key for relation Y.
So that given decomposition is losslessjoin decomposition.
R → P in Y

QR→S

S→Q

} are in Z and dependency preserving decomposition. Hence , C is the correct answer.