Syllogism — combine two “some” statements with a shared middle class Statements: • Some houses are offices. • Some offices are schools. Conclusions to evaluate: I. Some schools are houses. II. Some offices are houses. III. No house is school. IV. Some schools are offices.

Introduction / Context:
This exercise assesses how to read two independent some-type premises that meet at a middle term. The first links houses and offices; the second links offices and schools. The question is which conclusions are guaranteed without overreaching.

Given Data / Assumptions:

• H = houses, O = offices, S = schools.
• Some H are O.
• Some O are S.

Concept / Approach:
From some A are B you may always infer the symmetric some B are A, because it asserts the existence of elements in the intersection. Therefore, from some H are O, we also have some O are H (conclusion II). Likewise, from some O are S we get some S are O (conclusion IV). However, the two premises do not force a link between H and S, so neither an overlap nor a disjointness between H and S is necessary.

Step-by-Step Solution:

Verification / Alternative check:
Model: Let O contain two disjoint subsets, O1 overlapping H and O2 overlapping S, with O1 ∩ O2 = ∅. Then some H are O and some O are S both hold. II and IV are true (by symmetry), while I and III are false, confirming the result.

Why Other Options Are Wrong:

• Only I and II / Only I and IV: each includes I which is not compelled.
• Only II follows: omits IV, which is equally guaranteed.
• None follows: incorrect because II and IV are necessary.

Common Pitfalls:
Illicitly chaining some-premises to force an H–S overlap; assuming a universal negative without evidence.

Final Answer:
Only II and IV follow