In each question below, a few statements are followed by three conclusions.…

Concept

In categorical syllogisms, treat each universal statement as a set inclusion and each particular statement as proof that at least one member exists. A possibility conclusion is admissible when it can be added without contradicting any stated inclusion or exclusion.

This item explicitly stipulates existential import for universal statements: if all A are B, then A is non-empty and some B are A. Also, if some B are C and no C are D, those existing B–C members are not D.

Application

1. Let C, T, B, J, and K denote chairs, tables, bottles, jars, and buckets. From C ⊆ T and T ⊆ B, transitivity gives C ⊆ B. Because the stem stipulates that C is non-empty, choose c in C; then c is also in B. Hence some bottles are chairs, so conclusion II follows.

2. Some bottles are jars, so choose an existing member x in B ∩ J. No jar is a bucket, hence x is not in K. Thus x lies in B but not in K, so conclusion III follows.

3. No statement forbids T ∩ J. A table may be placed inside the jar region while every jar remains outside the bucket region and C ⊆ T ⊆ B is preserved. Therefore conclusion I is possible.

Cross-check

A consistent model can contain one chair–table–bottle member and one table–bottle–jar member, with every jar outside the bucket set. The explicit non-empty-class convention rules out an empty chair set; the model satisfies all four statements and supports conclusions I, II, and III.

Therefore, all conclusions follow.