Syllogism – Decide which conclusion(s) are forced: Statements: • Some Indians are educated. • Educated men prefer small families. Conclusions: (I) All small families are educated. (II) Some Indians prefer small families.

Difficulty: Medium

Correct Answer: Neither I nor II follows

Explanation:


Introduction / Context:
This problem checks careful reading of quantifiers and subgroup qualifiers. We have one existential about “Indians” and one conditional preference limited to “educated men”.



Given Data / Assumptions:

  • Some Indians are educated (∃ Indian ∩ Educated).
  • Educated men ⊆ PreferSmallFamilies.
  • No statement guarantees that the “some educated Indians” are men, nor that every small family is connected back to “educated”.


Concept / Approach:
(I) reverses the given direction (“educated men ⇒ prefer small families”) into a universal about all small families; this is a converse fallacy. (II) needs at least one Indian who is both educated and a man; “Some Indians are educated” does not require that the “some” are men.



Step-by-Step Solution:
To force (II), we would need ∃ (Indian ∩ Educated ∩ Man). The premises do not assert this.To force (I), we would need SmallFamily ⊆ Educated (or ⊆ EducatedMen), which is absent.



Verification / Alternative check:
Countermodel: All educated Indians are women; educated men (if any) are non-Indians. Then (II) fails. Also, there can be small families formed by uneducated persons, so (I) fails.



Why Other Options Are Wrong:
Any option claiming a forced conclusion ignores the missing links (gender condition for II; converse direction for I).



Common Pitfalls:
Forgetting subgroup qualifiers (“men”) and illicitly converting conditionals.



Final Answer:
Neither I nor II follows.

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