Syllogism — Decide which conclusion(s) must hold: Statements: • Some principals are teachers. • All teachers are students. Conclusions: I. All principals are students. II. Some students are principals.

Introduction / Context:
This problem combines a particular statement with a universal inclusion. The goal is to push the “some” individuals through the chain while avoiding unwarranted universal claims about all principals.

Given Data / Assumptions:

• S1: Some Principals are Teachers.
• S2: All Teachers are Students (Teachers ⊆ Students).
• Conclusions: I “All Principals are Students.” II “Some Students are Principals.”

Concept / Approach:
The subset relation allows transfer: those principals who are teachers are certainly students. That yields an existential overlap between Students and Principals. However, nothing says all Principals are Teachers (or Students), so the universal I does not follow.

Step-by-Step Solution:
1) From S1 pick x with Principal(x) and Teacher(x).2) From S2, Teacher(x) ⇒ Student(x).3) Hence Student(x) and Principal(x), proving II (Some Students are Principals).4) I would require every Principal to be a Student, which is not guaranteed.

Verification / Alternative check:
Diagram: Teachers inside Students; Principals overlaps Teachers partially. The overlap witnesses II; there may be Principals outside Teachers/Students, so I is not necessary.

Why Other Options Are Wrong:
Any option including I assumes a universal inclusion not present in the premises.

Common Pitfalls:
Generalizing from “some” to “all.”

Final Answer:
Only Conclusion II follows.