Some principals are teachers and all teachers are students; based on this, which of the given conclusions about principals and students logically follows?

Introduction / Context:
This syllogism style question involves three sets: principals, teachers and students. You must check which of the two conclusions about principals and students are logically forced by the given statements.

Given Data / Assumptions:

• Statement 1: Some principals are teachers.
• Statement 2: All teachers are students.
• Conclusion I: All principals are students.
• Conclusion II: Some students are principals.

Concept / Approach:
Some principals are teachers means there is at least one person who is both a principal and a teacher. All teachers are students means the entire set of teachers lies inside the set of students. By combining these, we consider what we can say about principals and students.

Step-by-Step Solution:
Step 1: From some principals are teachers, pick at least one person who belongs to both sets: principal and teacher. Step 2: From all teachers are students, anyone who is a teacher must also be a student. Step 3: Therefore the person who is both a principal and a teacher must also be a student. This means there exists at least one person who is both a principal and a student. Step 4: Thus some students are principals is definitely true, and conclusion II follows. Step 5: Conclusion I says all principals are students. We only know that some principals are teachers and thus students. There may be other principals who are not teachers and whose student status is unknown. So conclusion I is not forced.

Verification / Alternative check:
Construct an example. Let the set of principals be {p1, p2}, teachers be {p1, t1} and students be {p1, t1, s1}. Some principals (p1) are teachers, and all teachers are students. Here, some students (p1) are principals, so conclusion II holds. However, principal p2 is not necessarily a student in this example, so conclusion I fails. This confirms that only conclusion II is logically valid.

Why Other Options Are Wrong:
Option A chooses only conclusion I, which overgeneralises the relation between principals and students. Option C says both conclusions follow, which is not correct because we cannot include all principals. Option D says neither follows, which ignores the clear existence of at least one principal who is a student. Option E suggests an ambiguous either or, but the question requires the specific conclusion that holds, which is conclusion II.

Common Pitfalls:
A frequent mistake is to misread some as all and immediately assume that all principals are teachers or all principals are students. Another error is to ignore that there can be principals who are not teachers and whose relation to the student set is not defined by the given statements.

Final Answer:
The correct evaluation is that only conclusion II follows from the given statements.