Statements: 1) Some teachers are followers. 2) Some followers are famous. Conclusions: I. Some teachers are famous. II. Some followers are teachers. Choose the option that must follow.

Introduction / Context:Two “some” premises can be tricky because they establish existence but not necessarily intersection between the specific subsets mentioned. The test is to see whether we can deduce overlap where it is warranted and avoid it where it is not.

Given Data / Assumptions:

• Some Teachers are Followers (∃x ∈ Teachers ∩ Followers).
• Some Followers are Famous (∃y ∈ Followers ∩ Famous).

Concept / Approach:Conclusion II is directly supported: from the first premise, there exist followers who are teachers. But Conclusion I would require that at least one of the followers who is a teacher is also among the followers who are famous— which the premises do not guarantee.

Step-by-Step Solution:1) From Premise 1, pick t1 ∈ Teachers ∩ Followers. This witnesses Conclusion II: “Some Followers are Teachers.”2) Premise 2 provides some follower f1 ∈ Followers ∩ Famous. The premises do not assert t1 = f1, so we cannot claim a teacher who is famous.3) Therefore, Conclusion I is not necessary, while II is.

Verification / Alternative check:Model: Followers = {t1, f1}; Teachers = {t1}; Famous = {f1}. Both premises hold. II is true (t1 is a follower-teacher), but I is false (no teacher is famous). Hence only II follows.

Why Other Options Are Wrong:Claims that I follows assume the same element witnesses both premises; the data do not enforce that. “Both” overstates; “Neither” understates.

Common Pitfalls:Assuming that two separate existential statements necessarily refer to the same individual. That coincidence is not guaranteed.

Final Answer:Only Conclusion II follows.