GATE DA 2024 Set 1 — Question 54
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MSQ+2 / -0HardFirst-Order Predicate LogicPredicate LogicArtificial IntelligenceTranslations
Artificial Intelligence → Predicate Logic → First-Order Predicate Logic
Last updated
Question
Let be true if the ball is used in rugby and false otherwise.
Let be true if the ball is round and false otherwise.Consider the following logical sentences:
Which of the following choices is/are logical representations of the assertion,
"All balls are round except balls used in rugby"?
Let be true if the ball is round and false otherwise.Consider the following logical sentences:
Which of the following choices is/are logical representations of the assertion,
"All balls are round except balls used in rugby"?
Correct answer
(A) s1 ∧ s3; (C) s2 ∧ s3
Solution
The statement "All balls are round except balls used in rugby" implies two conditions:
1.If a ball is NOT used in rugby, it IS round. ()
2.If a ball IS used in rugby, it is NOT round (the exception). ()
Let's map these to the given sentences:- (Matches condition 1)
- (Contrapositive of , so )
- (Matches condition 2)
- (Contrapositive of , so )
- (A) : Contains both conditions. Correct.
- (B) : Equivalent to . Missing the exception part. Incorrect.
- (C) : Equivalent to . Contains both conditions. Correct.
- (D) : Equivalent to . Missing the general rule. Incorrect.
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 DA 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 Predicate Logic
2026 Set 1 Q13Which of the following algorithms is NOT an example of uninformed search?2026 Set 1 Q14Which of the following statements is NOT true? (The names of the predicates are intuitive.)2026 Set 1 Q23In the following table, the
Task column lists a few tasks related to machine learning. The…2026 Set 1 Q24Sentence is said to entail Sentence if whenever is TRUE, also must hold TRUE. Which…2026 Set 1 Q30Consider the game tree for a two-player turn-taking minimax game as shown in the figure. The value…