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GATE DA 2026 Q59: Tuples returned by a tuple relational calculus query

Question

Let there be two relations XX and YY as shown. XX has three columns PP, QQ and RR. YY has two columns PP and SS.

X
PQR
P1Q1R1
P2Q2R2
P3Q3R2
Y
PS
P110
P115
P220
P31

Consider that the following tuple relational calculus expression is evaluated.

{t∣t∈X∧∃z∈X (t[P]=z[P])∧∃m∈Y (m[P]=t[P]∧m[S]>1)}\{t \mid t \in X \wedge \exists z \in X\,(t[P] = z[P]) \wedge \exists m \in Y\,(m[P] = t[P] \wedge m[S] > 1)\}

The number of tuples that will be returned is __________. (Answer in integer)

Try it: numerical answer: type the value

Numerical answer. No negative marking.
Show answer and explanation

Answer: 2 to 3 (official GATE 2026 final answer key)

Concept used: Tuple relational calculus returns each tuple of X that satisfies the condition once.

First step: The middle condition is always true (z=tz = t); keep the X tuples whose P has a Y row with S > 1: P1 (10, 15) and P2 (20), not P3 (1).

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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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