Syllogism — Doors, Buses, Leaves, Flowers Statements: • All doors are buses. • All buses are leaves. • No leaf is a flower. Conclusions: I. No flower is a door. II. No flower is a bus. III. Some leaves are doors. IV. Some leaves are buses.
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ANone follows
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BOnly I and II follow
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COnly II and III follow
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DOnly II, III and IV follow
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EAll follow
Answer
Correct Answer: Only I and II follow
Explanation
Introduction / Context:This question uses two universal inclusions and one universal exclusion. The task is to infer which universal negatives are forced and whether any particular (“some”) statements can be deduced without explicit existence information.
Given Data / Assumptions:
- Doors ⊆ Buses ⊆ Leaves.
- Leaves ∩ Flowers = ∅.
Concept / Approach:When a class is a subset of a class disjoint from another, it is also disjoint from that other class. However, “All A are B” does not by itself guarantee existence of A or B, so you cannot conclude “Some B are A” unless a “some” premise provides existence.
Step-by-Step Solution:
I. Doors ⊆ Leaves and Leaves ∩ Flowers = ∅ ⇒ Doors ∩ Flowers = ∅ ⇒ “No flower is a door” follows.II. Buses ⊆ Leaves and Leaves ∩ Flowers = ∅ ⇒ Buses ∩ Flowers = ∅ ⇒ “No flower is a bus” follows.III. “Some leaves are doors” does not follow; existence of doors is not asserted by any premise (universal statements do not assure existence).IV. “Some leaves are buses” similarly does not follow without an explicit “some bus exists.”Verification / Alternative check:Build a model with empty Doors/Buses classes; the universal statements remain true, yet III and IV would be false, proving they are not logically necessary.
Why Other Options Are Wrong:
- Options listing III or IV assume existence not given by the premises.
- “All follow” overstates; only the two universal negatives are compelled.
Common Pitfalls:Committing the existential fallacy—deriving a particular conclusion (“some …”) from only universal premises.
Final Answer:Only I and II follow