Three statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.

Statements:
1. All teachers are students.
2. All principal are teachers.
3. Some principals are doctors.

Conclusions:
I. Some students are teachers.
II. No student is a doctor.
III. Some students are principals.