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)

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 / logic
1) 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 Answer
Only conclusion I follows.