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.
Verbal Reasoning
Logical Deduction
Difficulty: Medium
Choose an option
Answer
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 AnswerNeither I nor II follows.