Under the conventional existential-import rule used in aptitude-test…

CONCEPT

A universal affirmative proposition has the form “All S are P”, represented as S ⊆ P. In the conventional syllogism rules used in aptitude tests, the subject class S is treated as non-empty, so the universal affirmative has existential import.

Under subalternation, an A-form proposition therefore supports the corresponding I-form proposition “Some S are P”. It does not support the contrary E-form, the contradictory O-form, or an existence claim about the part of P outside S.

APPLICATION

1. Let S be the set of successful administrators and I be the set of intelligent people.

2. The premise “All successful administrators are intelligent” gives S ⊆ I.

3. By the conventional existential-import assumption, S is non-empty; choose an element x in S.

4. Since S ⊆ I, the same element x is also in I. Hence at least one successful administrator is intelligent.

CONTRAST

• “No successful administrator is intelligent” makes S and I disjoint, contrary to S ⊆ I with non-empty S.

• “Some successful administrators are not intelligent” requires an element of S outside I, contradicting S ⊆ I.

• “Some intelligent people are not successful administrators” needs an element in I outside S; the premise does not guarantee that region is occupied.

CROSS-CHECK

Draw the S circle entirely inside the I circle and place one witness in S. That witness necessarily lies in both circles, while no witness is forced into the I-only region.

Therefore, the statement that follows is “Some successful administrators are intelligent”.