GATE CS 2025 Set 1 — Question 48
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MSQ+2 / -0MediumPredicate Logic & QuantifiersMathematical LogicEngineering Mathematics
Engineering Mathematics → Mathematical Logic → Predicate Logic & Quantifiers
Last updated
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:
- : is the mother of
- : and are not equal
Correct answer
(B) ∀ x ∃ y [mother(y, x) ∧ ∀ z(noteq(z, y) arrow ¬ mother(z, x))]; (D) ∀ x ∃ y [mother(y, x) ∧ ¬ ∃ z(noteq(z, y) ∧ mother(z, x))]
Solution
The statement "Everyone has exactly one mother" means for every person , there exists a person such that is the mother of , and for any person , if is the mother of , then must be .
- Option (B): . This says for every , there is a who is the mother, and for any different from , is not the mother. This correctly represents existence and uniqueness.
- Option (D): . The second part is logically equivalent to , which simplifies to . This also correctly represents existence and uniqueness.
- Option (A) only says everyone has at least one mother and at least one person who is not their mother.
- Option (C) is a tautology that doesn't guarantee existence or uniqueness.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CS question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Mathematical Logic
2026 Set 2 Q3A day can only be cloudy or sunny. The probability of a day being cloudy is , independent of…2026 Set 2 Q5‘When it is raining, peacocks dance.’ Based only on this sentence, which one of the following…2026 Set 2 Q8Figures (i) and (ii) represent intercity highway systems. The black dots represent cities and the…2026 Set 1 Q10An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice…2026 Set 2 Q10An unbiased six-faced dice whose faces are marked with numbers 1, 2, 3, 4, 5, and 6 is rolled twice…