Which of the following statements is contrary to the statement—"No football…

Concept

Categorical propositions are classified by quantity (universal or particular) and quality (affirmative or negative). In the traditional square of opposition, the A-form “All S are P” and the E-form “No S are P” form the universal pair that cannot both be true, although both can be false.

Application

The given statement, “No football players are kind-hearted human beings,” has the universal-negative E-form. The required opposite must keep the universal quantity and change the quality to affirmative: “All football players are kind-hearted human beings.”

Contrast

• “Some football players are kind-hearted human beings” is an I-form: particular and affirmative; it asserts that at least one member lies in both classes.

• “Some football players are not kind-hearted human beings” is an O-form: particular and negative; it asserts that at least one football player lies outside the other class.

• “No kind-hearted human beings are football players” is an E-form: universal and negative; reversing the class names preserves the same complete exclusion.

• “All football players are kind-hearted human beings” is an A-form: universal and affirmative; it places the entire football-player class inside the other class.

Cross-check

The required pair must be universal and differ only in affirmative versus negative quality. The E-to-A change meets that test, so the required statement is “All football players are kind-hearted human beings.”