Skip to content
GATEiit

GATE CSE 2021 Set 1 Q43: Lossless or lossy: two decompositions of R(P,Q,S,T,X,Y,Z,W)

Question

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 \to X; \quad P \to YX; \quad Q \to Y; \quad Y \to ZW

Consider the decomposition of the relation RR 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: \; 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: \; R = [(P, Q, S);\ (T, X);\ (Q, Y);\ (Y, Z, W)]

Which one of the following options is correct?

Try it: multiple choice: exactly one correct option

Select one option
Wrong answer costs 2/3 mark in GATE.
Show answer and explanation

Answer: A (official GATE 2021 final answer key)

Concept used: Join components pairwise: a binary join is lossless when the common attributes form a key of one side.

First step: In D2D_2, list the attributes that the component (T,X)(T, X) shares with the other three components; in D1D_1, check that PT→XPT \to X holds.

Full step-by-step solution

Detailed working, common mistakes and linked mock tests will be available with a free GATEiit account. Log-in is coming soon.

Share this question

WhatsAppDownload image

Source: official GATE 2021 Set 1 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key

More Databases PYQs

PracticePractise Databases questions →Full paperAll GATE CSE 2021 Set 1 questions →