Set–subset reasoning with quantifiers: 'Many scooters are trucks' and 'All trucks are trains' — identify which conclusion is logically valid (Some scooters are trains; No truck is a scooter)
Verbal Reasoning
Logical Deduction
Difficulty: Easy
Choose an option
Answer
Correct Answer: Only conclusion I follows
Explanation
Given data
- Premise 1: Many (hence, at least some) Scooters are Trucks.
- Premise 2: All Trucks ⟶ Trains.
- Conclusions:
- I: Some Scooters are Trains.
- II: No Truck is a Scooter.
Concept/Approach (why this method)
Translate 'many' to 'at least some' and use transitivity: If some A are B and all B are C, then those 'some A' are also C.
Step-by-Step calculation / logic1) From Premise 1, pick a scooter that is a truck.2) From Premise 2, that truck is a train.3) Therefore, at least one scooter is a train ⇒ Conclusion I is necessary.4) Conclusion II contradicts Premise 1 (which states some overlap) ⇒ false.
Verification/Alternative
Venn chaining: Scooters ↔ (some) Trucks ↔ Trains ensures non-empty intersection of Scooters and Trains.
Common pitfalls
- Reading 'many' as 'most' or 'all' (not required; only 'some' is needed).
Final AnswerOnly conclusion I follows.