The GATE Grind

GATE 2021 CS – Question 43

Databases · Integrity Constraints and Normal Forms · 2 marks · Multiple choice

Consider the relation $R(P,Q,S,T,X,Y,Z,W)$ with the following functional dependencies.
$PQ \rightarrow X;\ P \rightarrow YX;\ Q \rightarrow Y;\ Y \rightarrow ZW$
Consider the decomposition of the relation $R$ into the constituent relations according to the following two decomposition schemes.
$D_1$: $R = [(P,Q,S,T);\ (P,T,X);\ (Q,Y);\ (Y,Z,W)]$
$D_2$: $R = [(P,Q,S);\ (T,X);\ (Q,Y);\ (Y,Z,W)]$
Which one of the following options is correct?

  1. $D_1$ is a lossless decomposition, but $D_2$ is a lossy decomposition.
  2. $D_1$ is a lossy decomposition, but $D_2$ is a lossless decomposition.
  3. Both $D_1$ and $D_2$ are lossless decompositions.
  4. Both $D_1$ and $D_2$ are lossy decompositions.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $D_1$ is a lossless decomposition, but $D_2$ is a lossy decomposition.

Explanation

Chase test: in $D_1$, P and T are shared with (P,Q,S,T), P->X, Q->Y and Y->ZW let all attributes be filled in one row, so it is lossless. In $D_2$, (T,X) has no attribute in common that determines it (T is not determined), so the chase fails and it is lossy.