Statements: All dolls are windows. All bottles are windows. All cars are…

Concept: For two universal affirmative premises 'All A are B' and 'All B are C' sharing the middle term B, the chain combines validly into 'All A are C' precisely when B is distributed -- i.e. functions as the SUBJECT -- in at least one of the two premises (being only the predicate of a universal premise never distributes a term). A universal affirmative also converts per accidens, under the standard exam convention that every named category is non-empty: 'All A are B' gives 'Some B are A.' But when two universal premises share a term that is undistributed in BOTH -- i.e. it is only ever their predicate, never a subject -- the premises cannot be combined at all: no conclusion, universal or particular, follows about their other terms.

1. 'All cars are bottles' and 'All bottles are windows' share the middle term 'bottles': it is the predicate (undistributed) in the first premise but the subject (distributed) in the second. Since the middle term is distributed at least once, the chain is valid, so 'All cars are windows' follows.

2. 'All cars are windows' is a universal affirmative statement, so it converts per accidens to 'Some windows are cars,' with the terms reversed and the quantity weakened to particular.

3. 'All dolls are windows' and 'All cars are windows' both use 'windows' only as their predicate -- it is undistributed in each -- so these two premises cannot be combined into any conclusion about cars and dolls, universal or particular.

Cross-check: place 'windows' as the outer circle. 'Bottles' sits inside it, with 'cars' inside 'bottles' -- fixing the cars-windows relationship exactly as derived. 'Dolls' sits inside 'windows' too, but in a region the premises never pin relative to 'bottles' or 'cars' -- so 'cars' and 'dolls' may or may not overlap, confirming that no fixed relationship between them is guaranteed.

Only the chain conclusion and its converse are guaranteed by the premises; the claim linking cars and dolls is not.