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GATE CSE 2025 Session 1 Q48: Predicate logic for "Everyone has exactly one mother"

Question

Which of the following predicate logic formulae/formula is/are CORRECT representation(s) of the statement: "Everyone has exactly one mother"?

The meanings of the predicates used are:

• mother(y,x)mother(y, x): yy is the mother of xx • noteq(x,y)noteq(x, y): xx and yy are not equal

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: B, D (official GATE 2025 final answer key)

Concept used: "Exactly one" = there is one, and anyone else is not.

First step: Write it as: for every xx there is a yy that is xx's mother, and every zz different from yy is not xx's mother; then compare each option (note ¬∃z (P∧Q)≡∀z (P→¬Q)\neg\exists z\,(P \land Q) \equiv \forall z\,(P \to \neg Q)).

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Source: official GATE 2025 Session 1 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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