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Contrived universe test: with ‘‘All trucks fly’’ and ‘‘Some scooters fly’’ evaluate whether it follows that all trucks are scooters or that some scooters do not fly.

Difficulty: Easy

Correct Answer: Neither I nor II follows

Explanation:

Examine the logical independence of the classes Trucks, Scooters, and the property Fly.

  • Premise 1: All trucks fly, so Trucks ⊆ Fly.
  • Premise 2: Some scooters fly, so Scooters ∩ Fly ≠ ∅.
  • Conclusions: I. All trucks are scooters. II. Some scooters do not fly.

Concept/Approach
Subset to the property Fly does not create a subset relation between Trucks and Scooters, and existence of flying scooters does not imply existence of non flying scooters.
Testing conclusion I
Nothing links Trucks to Scooters. Trucks could be entirely separate from Scooters yet still fly. Hence I does not follow.
Testing conclusion II
We only know some scooters do fly. The set of scooters could all be flyers, so the existence of non flying scooters is not guaranteed. Hence II does not follow.
Verification/Alternative
Model: Trucks = {t1}, Scooters = {s1}, Fly = {t1, s1}. Both premises hold; I is false and II is false.
Common pitfalls
Reading extra relations between subject classes that are not supplied by the premises.
Final Answer
Neither I nor II follows.
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