Syllogism — Identify necessary conclusions: Statements: • All teachers are experienced. • Some teachers are spinsters. Conclusions: I. Some experienced are spinsters. II. Some spinsters are experienced.

Introduction / Context:
The premises combine a universal inclusion with a particular existence about the same subject class (“teachers”). We must test two closely related existential conclusions.

Given Data / Assumptions:

• Teachers ⊆ Experienced.
• Some Teachers are Spinsters (Teachers ∩ Spinsters ≠ ∅).

Concept / Approach:
Take the individuals that are both Teachers and Spinsters. Because every Teacher is Experienced, those individuals are also Experienced. Hence an overlap between Experienced and Spinsters exists, and reciprocally some Spinsters are Experienced.

Step-by-Step Solution:
1) From “Some Teachers are Spinsters,” pick an element x with Teacher(x) ∧ Spinster(x).2) Teachers ⊆ Experienced ⇒ Experienced(x).3) Therefore Experienced ∩ Spinsters ≠ ∅, which simultaneously proves “Some experienced are spinsters” (I) and “Some spinsters are experienced” (II).

Verification / Alternative check:
Draw Teachers inside Experienced; mark an overlap between Teachers and Spinsters. That overlap sits inside Experienced ∩ Spinsters, verifying both conclusions.

Why Other Options Are Wrong:
Any single-conclusion or “either-or” option underplays the guaranteed two-way existential overlap.

Common Pitfalls:
Forgetting that an existential statement about a subset transfers through a universal inclusion to the superset.

Final Answer:
Both conclusion I and II follow.