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GATE DA 2026 Q48: Which first-order logic statements are not valid

Question

Let P(x)P(x) be a predicate.

Which of the following statements is/are NOT valid in first-order logic?

Try it: multiple select: one or more correct options

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Answer: B, C, D (official GATE 2026 final answer key)

Concept used: A valid sentence is true in every interpretation (first-order domains are non-empty).

First step: If PP holds for everything it holds for something, so A is valid; find a domain where some but not all elements satisfy PP to break B and C, and one where all do to break D.

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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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