GATE CS 2026 Set 2 — Question 11
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Engineering Mathematics → Mathematical Logic → Predicate Logic & Quantifiers
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Question
For two different persons and , the predicate denotes that knows .
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?
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?
Correct answer
(A) (∃ y)(∀ x) ((x ≠ y) arrow (M(x, y) ∧ ¬ M(y, x)))
Solution
Let the person described be .
This matches option (A).
1."There is a person": This implies existence, so we use the existential quantifier .
2."who does not know anyone else": This means for all other persons (where ), does not know . This is represented as .
3."but that person is known by everyone else": This means for all other persons (where ), knows . This is represented as .
Combining these conditions:This matches option (A).
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