Syllogism – Overlap vs. disjoint “some” sets: Statements: 1) Some teachers are followers. 2) Some followers are famous. Conclusions: I) Some teachers are famous. II) Some followers are teachers. Choose the correct logical result.

Introduction / Context:Two particular premises (“some … are …”) do not guarantee that the two “some” subsets intersect unless explicitly connected.

Given Data / Assumptions:

• ∃ T∩Foll (some Teachers are Followers).
• ∃ Foll∩Fam (some Followers are Famous).

Concept / Approach:Conclusion II simply rephrases one premise: if some Teachers are Followers, the same elements witness “Some Followers are Teachers.” But Conclusion I requires the intersection of the two particular subsets inside Followers.

Step-by-Step Solution:For II: Using symmetry of “some,” from T∩Foll ≠ ∅ we get Foll∩T ≠ ∅, so II necessarily follows.For I: We would need T∩Fam ≠ ∅. Premises only ensure T∩Foll ≠ ∅ and Foll∩Fam ≠ ∅, which may be disjoint pieces of Followers; hence I is not forced.

Verification / Alternative check:Create Followers with two disjoint parts: one overlapping Teachers, another overlapping Famous. Both premises hold, yet no Teacher is Famous, falsifying I.

Why Other Options Are Wrong:Claiming I follows assumes an unjustified intersection. “Both follow” and “Neither follow” are also contradicted by the analysis.

Common Pitfalls:Believing that two “some” statements with a common middle term force a three-way overlap.

Final Answer:Only Conclusion II follows.