Syllogism — Premises: Some teachers are students. All students are girls. Conclusions: (I) All teachers are girls. (II) Some girls are teachers. (III) Some girls are students. (IV) All students are teachers.

Introduction / Context:
We combine one existential and one universal premise and check which conclusions are necessary.

Given Data / Assumptions:

• Some Teachers are Students.
• All Students are Girls.

Concept / Approach:
Let T = Teachers, S = Students, G = Girls. From 'Some T are S' and 'S ⊆ G', we infer (II) Some girls are teachers (those teacher-students are girls) and (III) Some girls are students (since some students exist). The universal claims (I) and (IV) are not supported.

Step-by-Step Solution:

Verification / Alternative check:
Construct a model with many teachers not students and many girls not students; (II) and (III) remain forced while (I) and (IV) fail.

Why Other Options Are Wrong:
Options including (I) or (IV) assert unsupported universals.

Common Pitfalls:
Overgeneralizing from existence to universals; keep directions of subset relations straight.

Final Answer:
Only (II) and (III) follow.