Problem 8 - Entrance Test

Some students are athletes. All athletes are healthy. Which conclusion necessarily follows?

A. All healthy people are studentsB. Some students are healthyC. No student is healthyD. All students are athletes

Correct: B

From 'Some S are A' and 'All A are H', we can conclude 'Some S are H' by the chain rule. The particular affirmative premise ensures that at least some students share the property of being athletes, and since all athletes are healthy, those students are also healthy. This is a valid syllogism (DAR-3 in figure 3). The other options either reverse the relationship or make unsupported negative claims.