Statements: Some pictures are frames. Some frames are idols. All idols are…

Concept: A particular statement 'Some A are B' converts to 'Some B are A' (conversion preserves the particular form), and — provided A is non-empty — a universal statement 'All A are B' has the limited converse 'Some B are A'. Two particular statements never combine to give a valid conclusion, and when one statement is particular and the other universal, any valid conclusion must be particular and must drop the shared (middle) term.

1. 'Some frames are idols' is particular; its direct converse, 'Some idols are frames' (Conclusion III), is always valid on its own.

2. Combine 'Some frames are idols' (particular) with 'All idols are curtains' (universal) through the shared term 'idols': since one statement is particular, the conclusion is particular and drops 'idols', giving 'Some frames are curtains'.

3. 'Some frames are curtains' is particular; its converse, 'Some curtains are frames' (Conclusion II), is therefore also valid.

4. Reaching Conclusion I, 'Some curtains are pictures', would need 'Some pictures are frames' to combine with 'Some frames are curtains' — but both of these are particular statements, and two particular statements never yield a valid conclusion, so Conclusion I does not follow.

Cross-check with a concrete case: let pictures = {A, E}, frames = {A, B}, idols = {B, C}, curtains = {B, C, D}. This satisfies all three statements ('Some pictures are frames' via A; 'Some frames are idols' via B; 'All idols are curtains' since {B, C} is a subset of {B, C, D}). Here curtains and frames share B (Conclusion II holds) and idols and frames share B (Conclusion III holds), but curtains and pictures share nothing (Conclusion I fails) — confirming that only II and III are guaranteed.

So exactly Conclusions II and III follow.