Consider the relation \(R(P,Q,S,T,X,Y,Z,W)\) with the following functional…

GATE · 2021 · CS · Set 1 · Computer Science & IT

Consider the relation R(P,Q,S,T,X,Y,Z,W)R(P,Q,S,T,X,Y,Z,W)  with the following functional dependencies.

PQ→X;P→YX;Q→Y;Y→ZWPQ\rightarrow X;\quad P\rightarrow YX;\quad Q\rightarrow Y; \quad Y\rightarrow ZW

 Consider the decomposition of the relation R into the constituent relations according to the following two decomposition schemes.

D1:R=[(P,Q,S,T);  (P,T,X);  (Q,Y);  (Y,Z,W)]D_1:\quad R=[(P,Q,S,T);\;(P,T,X);\;(Q,Y);\;(Y,Z,W)]

D2:R=[(P,Q,S);  (T,X);  (Q,Y);  (Y,Z,W)]D_2:\quad R=[(P,Q,S);\;(T,X);\;(Q,Y);\;(Y,Z,W)]

Which one of the following options is correct?

  1. A.

    D1D_1  is a lossless decomposition, but D2D_2 is a lossy decomposition

  2. B.

    D1D_1  is a lossy decomposition, but D2D_2 is a lossless decomposition

  3. C.

    Both D1D_1 and D2D_2 are lossless decompositions

  4. D.

    Both D1D_1 and D2D_2 are lossy decompositions

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