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Particular–universal with common middle: Given 'Some dedicated souls are angels' and 'All social workers are angels', analyze whether the conclusions (I) 'Some dedicated souls are social workers' and (II) 'Some social workers are dedicated souls' are logically compelled.

Difficulty: Medium

Correct Answer: Neither I nor II follows

Explanation:

Given data

  • Premise 1: Some Dedicated Souls ⊆ Angels (particular inclusion).
  • Premise 2: Social Workers ⊆ Angels (universal inclusion).
  • Conclusions: (I) Some Dedicated Souls are Social Workers. (II) Some Social Workers are Dedicated Souls.

Concept/Approach

Sharing a common superset (Angels) does not force overlap between the two subsets. Particular conclusions about intersection need evidence of direct overlap, not merely co-membership of a larger set.

Step-by-step evaluation

1) DS ⊆ Angels (for some elements), and SW ⊆ Angels.2) DS and SW might be disjoint subsets inside Angels.3) Therefore neither (I) nor (II) is necessary.

Verification/Alternative

Countermodel: Angels = {a1, a2}, DS = {a1}, SW = {a2}. Premises true; both conclusions false.

Common pitfalls

  • Assuming common membership implies intersection (subset fallacy).

Final Answer
Neither I nor II follows.

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