Syllogism – Universal subset with unrelated particular: Statements: 1) All trees are leaves. 2) Some fruits are leaves. Conclusions: I) Some fruits are trees. II) Some leaves are trees. Identify which conclusions are compelled by the premises.

Difficulty: Medium

Correct Answer: Only Conclusion II follows

Explanation:


Introduction / Context:
This item probes existential import and subset reasoning. Premise (1) nests Trees within Leaves; Premise (2) makes Fruits overlap Leaves.



Given Data / Assumptions:

  • Trees ⊆ Leaves.
  • ∃ Fruits∩Leaves.


Concept / Approach:
Conclusion I requires Fruits∩Trees ≠ 0, which is not guaranteed. Conclusion II claims the existence of at least one Tree (hence a Leaf that is a Tree). In standard exam convention, universal classes are assumed non-empty unless stated otherwise, allowing II.



Step-by-Step Solution:
C1: “Some fruits are trees” – not forced; the fruit-leaf overlap can be outside Trees entirely.C2: “Some leaves are trees” – with non-emptiness assumed for the class Trees, at least one Tree exists and is a Leaf, so II follows.



Verification / Alternative check:
Countermodel for I: Place Fruits in the leaves region disjoint from Trees. Premises hold; I fails. For II, any non-empty Trees set suffices.



Why Other Options Are Wrong:
“Both” and “Only I” are too strong; “Neither” ignores the standard non-emptiness convention used in reasoning questions.



Common Pitfalls:
Confusion over existential import. Many learners incorrectly try to infer I from the separate facts about Leaves.



Final Answer:
Only Conclusion II follows.

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