Four sets of three statements each are given below. Take these statements to…

A categorical syllogism with two universal-affirmative premises sharing one middle term (“all A are B”, “all B are C”) validly yields “all A are C” — the chain must run in the same subject-to-predicate direction as the premises, through the shared middle term. Two things break this: reversing the derived relationship (a converse fallacy — “all C are A” does NOT follow from “all A are C”), and a particular premise (“some X are Y”), which leaves its middle term undistributed and permits no universal conclusion at all.

1. Tables/chairs/cupboards statement: the premises chain cupboards → tables → chairs, giving “all cupboards are chairs.” The stated third line, “all chairs are cupboards,” reverses this — a converse fallacy, so it is NOT implied.

2. J/K/M statement: the premises chain J’s → K’s → M’s, giving “all J’s are M’s.” The stated third line, “all M’s are J’s,” reverses this — again a converse fallacy, so it is NOT implied.

3. Apples/bananas/red statement: the premises chain bananas → apples → red through the shared middle term “apples,” giving “all bananas are red” — exactly the stated third line, in the same direction as the premises, so it IS implied.

4. Locks/keys/balls statement: the second premise, “some balls are keys,” is particular, so the middle term “keys” is undistributed. No universal relationship between locks and balls can be derived, so “all locks are balls” is NOT implied.

Cross-check by tracing the subset direction independently for each pair: only the bananas → apples → red chain preserves the same subset order from both premises through to the stated conclusion, with no reversal and no undistributed middle term — confirming the apples/bananas/red statement as the only one where the third statement follows from the first two.

So the alternative built on the apples/bananas/red statement is the one in which the third statement is implied by the first two.