GATE DA 2026 Q42: Output of a relational algebra expression with natural joins

Database Management and Warehousing
2 marks
MCQ
−2/3 if wrong

Consider the given relations $X$ , $Y$ and $Z$ . The relation $X$ has three columns $P$ , $Q$ and $R$ . The relation $Y$ has three columns $P$ , $Q$ and $S$ . The relation $Z$ has two columns $P$ and $T$ .

X
P	Q	R
P1	Q1	R1
P2	Q2	R2
P3	Q3	R2

Y
P	Q	S
P1	Q1	2
P1	Q2	5
P2	Q1	6
P3	Q3	1

Z
P	T
P1	T1
P3	T2
P4	T3
P4	NULL

Consider the relational algebra expression

$\Pi_{PRS}\left[\left(\sigma_{(Q = Q3 \,\vee\, R = R2)}[X \bowtie Y]\right) \bowtie \left(\sigma_{(S > 1)}[Y \bowtie Z]\right)\right]$

where $\bowtie$ denotes natural join operation.

Which of the following options is the correct output for the given expression?

Try it: multiple choice: exactly one correct option

Wrong answer costs 2/3 mark in GATE.

Show answer and explanation

Answer: D (official GATE 2026 final answer key)

Concept used: Natural join matches on all common columns; evaluate each side, then join on P, Q and S.

First step: $X \bowtie Y$ (on P, Q) gives (P1, Q1, R1, 2) and (P3, Q3, R2, 1); the selection keeps only (P3, Q3, R2, 1), whose S = 1 cannot appear on the right side.

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Source: official GATE 2026 DA question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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GATE DA 2026 Q42: Output of a relational algebra expression with natural joins

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