GATE CSE 2026 Session 2 Q11: Predicate logic: someone known by all who knows no one

For two different persons $x$ and $y$ , the predicate $M(x, y)$ denotes that $x$ knows $y$ . Consider the following statement.

There is a person who does not know anyone else, but that person is known by everyone else.

Which one of the following expressions represents the above statement?

Try it: multiple choice: exactly one correct option

Wrong answer costs 1/3 mark in GATE.

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Answer: A (official GATE 2026 final answer key)

Concept used: Translating English to first-order logic: "there is a person" is $\exists$ , "everyone else" is $\forall$ with $x \neq y$ .

First step: Let $y$ be the special person; then for every other $x$ , $x$ knows $y$ and $y$ does not know $x$ .

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Source: official GATE 2026 Session 2 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key