Syllogism — evaluate necessary conclusions from partial overlaps Statements: • Some clothes are marbles. • Some marbles are bags. Conclusions to evaluate: I. No cloth is a bag. II. All marbles are bags. III. Some bags are clothes. IV. No marble is a cloth.

Difficulty: Easy

Correct Answer: None follows

Explanation:


Introduction / Context:
This item checks your understanding of what can be guaranteed from two independent some-type statements. A common mistake is to chain two overlaps through a middle class and conclude an overlap between the outer classes. Without explicit linkage, that inference is not valid.



Given Data / Assumptions:

  • C = clothes, M = marbles, B = bags.
  • Some C are M. So C ∩ M is nonempty.
  • Some M are B. So M ∩ B is nonempty.
  • No other relations are specified.


Concept / Approach:
A statement of the form some A are B only ensures a nonempty intersection between A and B. Two such statements sharing a middle term (here M) do not force the outer sets to overlap. Therefore conclusions asserting no or some between C and B must be rejected unless forced by the premises. Universal statements like all M are B are also not justified by a mere some relation.



Step-by-Step Solution:

Conclusion I (No cloth is a bag) is not necessary. It could be that the marbles which are clothes are the very marbles which are bags, yielding some C ∩ B, contradicting I. Hence I does not follow.Conclusion II (All marbles are bags) strengthens a some statement to all and is not warranted. It does not follow.Conclusion III (Some bags are clothes) is tempting, but the two intersections could involve disjoint parts of M, so C and B may never meet. III does not follow.Conclusion IV (No marble is a cloth) is outright contradicted by the first premise, which guarantees at least one marble that is a cloth. So IV cannot follow.


Verification / Alternative check:
Model: Let M = {m1, m2}. Let C = {m1}. Let B = {m2}. Then some C are M (via m1) and some M are B (via m2) hold, while I–IV are all false or not forced, confirming that none follows.



Why Other Options Are Wrong:

  • Only either I or IV / only either I or II / only either I or III: each claims that exactly one of the listed conclusions must follow; in fact, none is necessary.
  • None of these: option C already states the correct outcome.


Common Pitfalls:
Assuming transitivity for some-statements; overlooking that IV directly contradicts the first premise.



Final Answer:
None follows

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