Statements: All aeroplanes are trains. Some trains are chairs. Conclusions: i.…

Concept

A conclusion linking the two end terms of two premises through a shared middle term is valid only if that middle term is distributed (refers to its full class) in at least one premise. Independently of that rule, any single premise can also be immediately converted on its own: a universal affirmative ('All A are B') validly converts to a particular statement with the terms swapped ('Some B are A'), and a particular affirmative ('Some A are B') validly converts to ('Some B are A') as well.

Application

1. Classify the two premises: 'All aeroplanes are trains' is a universal affirmative (aeroplanes distributed, trains not distributed, since trains is the predicate); 'Some trains are chairs' is a particular affirmative (neither term distributed).

2. Check the middle term 'trains' for distribution across the two premises: it is undistributed as the predicate of the first premise and undistributed as the subject of the second (particular) premise -- so it is undistributed in both.

3. Because the middle term is never distributed, no conclusion directly relating 'aeroplanes' and 'chairs' can be drawn, ruling out any conclusion that pairs the two end terms.

4. Apply conversion to each premise on its own: converting 'All aeroplanes are trains' gives 'Some trains are aeroplanes'; converting 'Some trains are chairs' gives 'Some chairs are trains'. Both conversions are valid immediate inferences, independent of the middle-term distribution check above.

Cross-check

A quick Venn sketch confirms it: chairs and aeroplanes can occupy entirely separate parts of the trains circle, so a direct aeroplane-chair relationship is never guaranteed -- but each premise's own converse is guaranteed regardless of how the diagram is drawn. So only the two converses hold.