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GATE CSE 2026 Session 1 Q30: Which functional dependency inferences always hold

Question

Let PP, QQ, RR and SS be the attributes of a relation in a relational schema. Let X→YX \to Y indicate functional dependency in the context of a relational database, where X,Y⊆{P,Q,R,S}X, Y \subseteq \{P, Q, R, S\}.

Which of the following options is/are always true?

Try it: multiple select: one or more correct options

Select one or more options
Select all correct options. No negative marking, no partial marks.
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Answer: C, D (official GATE 2026 final answer key)

Concept used: Armstrong's axioms: augmentation and union are sound; a determinant cannot be split.

First step: Augment P→RP \to R with QQ to get PQ→RPQ \to R, and test A and B with a small counterexample relation.

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Source: official GATE 2026 Session 1 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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