If the statement—"Some athletes are kind human beings"—is given as true, which…

Concept

A particular affirmative proposition, ‘Some S are P,’ asserts that at least one witness belongs to both classes S and P.

Its contradictory is the universal negative, ‘No S is P,’ which asserts that the intersection of S and P is empty. Contradictory propositions cannot both be true.

Application

1. Let A be the class of athletes and K the class of kind human beings.

2. The premise gives a witness x such that x belongs to both A and K, so the intersection A ∩ K is non-empty.

3. The statement ‘No athletes are kind human beings’ requires A ∩ K to be empty.

4. The same intersection cannot be both non-empty and empty; therefore that universal negative is false whenever the premise is true.

Cross-check and contrast

• ‘Some athletes are not kind human beings’ may still hold for another athlete; the premise does not describe every athlete.

• ‘All athletes are kind human beings’ is not established by one witness, but the premise alone does not make it false.

• ‘Some kind human beings are athletes’ restates the same witness with the class names reversed, because intersection membership is symmetric.

Hence, the statement immediately inferred to be false is ‘No athletes are kind human beings.’