Which conclusion would follow on the basis of given statements. Assume that…

Syllogism conclusions are tested with Venn diagrams drawn to satisfy every given statement. A definite conclusion (a plain "all/some/no X are Y" claim) follows only if it is true in every such diagram. A possibility conclusion ("X are Y is a possibility") follows if at least one valid diagram can be drawn where it holds, even if other valid diagrams make it false.

1. No A is B means no single object can belong to both A and B at once.

2. Some B are C means at least one object, call it p, belongs to both B and C.

3. All C are D means every object in C, including p, also belongs to D; so p belongs to B, C, and D together (and, being in B, p itself cannot belong to A).

4. No statement forbids placing a second, separate object, q, in both A and D while keeping q out of B and out of C, and no statement forces every object in A to also lie in C; adding q this way still satisfies "No A is B" (q is not in B) and leaves "Some B are C" and "All C are D" unaffected (already satisfied by p), so the whole diagram remains valid.

This second object q settles both conclusions at once: q belongs to A and D, so "Some A are D" is realized in this valid diagram, which is exactly what conclusion I claims as a possibility. At the same time, q belongs to A but not to C, so "All A are C" is false in this very same valid diagram; since a definite conclusion must hold in every valid diagram and this one diagram alone breaks it, "All A are C" cannot be a definite conclusion.

Only conclusion I follows.