Statements: No car is bike. Some bikes are trucks. Conclusions: I. No car is truck. II. Some trucks are not cars. III. Some bikes are not cars
Correct answer: C. II and III
- A. Only III
- B. Only II
- C. II and III
- D. I and III
Explanation
The correct answer is Option C: 'II and III'. Let's break down each conclusion:Conclusion I: 'No car is truck.' This conclusion is incorrect because the statements do not provide enough information to confirm that no cars are trucks. The statements only say 'No car is bike' and 'Some bikes are trucks,' which does not preclude the possibility of some cars being trucks.Conclusion II: 'Some trucks are not cars.' This conclusion can be inferred. Since no cars can be bikes, and some bikes are trucks, there must be some trucks that do not overlap with cars.Conclusion III: 'Some bikes are not cars.' This conclusion is directly supported by the statement 'No car is bike,' meaning that all bikes are not cars.Therefore, only conclusions II and III are valid based on the given statements.
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About Logical Deductions
Logical deductions require conclusions to be drawn from stated facts, conditions and relationships without adding outside information. The work includes handling all, some and none statements, necessary and sufficient conditions, ordering restrictions, true or false conclusions, and the difference between what must be true and what could be true.
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