Read the following statements and determine which inference(s) logically…

Concept

In a categorical syllogism, “All A are B” places class A wholly inside class B. Under the stated traditional aptitude-test convention, named classes are non-empty, so “Some B are A” follows from that universal statement.

An existential statement such as “Some B are C” converts validly to “Some C are B.” However, overlap between B and C does not force the subset A to overlap C.

Application

1. Inference I (“All scientists are smart”) does not follow: the premises place scientists inside researchers, but do not place every scientist inside the smart group.

2. Inference II (“Some scientists are smart”) does not follow: the smart researchers may lie outside the scientist subset.

3. Inference III (“Some smart people are researchers”) follows by converting “Some researchers are smart.”

4. Inference IV (“Some researchers are scientists”) follows because scientists form a non-empty subset of researchers under the stated convention.

Cross-check

Take researchers as {r1, r2}, scientists as {r1}, and smart people as {r2}. Both premises hold. Inference III and inference IV hold, while inference I and inference II fail.

Therefore, only inferences III and IV follow.