Among the following propositions two are related in such a way that they…

Concept: the square of opposition

Traditional logic sorts a categorical proposition by quantity (universal or particular) and by quality (affirmative or negative). That gives four standard forms: A, the universal affirmative, "All S are P"; E, the universal negative, "No S is P"; I, the particular affirmative, "Some S are P"; and O, the particular negative, "Some S are not P".

Two propositions are contrary when they cannot both be true yet can both be false. On the square of opposition this relation holds only between the two universals, A and E. The neighbouring relations behave differently: contradictories (A with O, E with I) can be neither both true nor both false; subcontraries (I with O) can both be true but cannot both be false; subalterns (A with I, E with O) can both be true and can both be false.

Application to this question

1. Classify each proposition by quantity and quality. "Every student is attentive" is universal and affirmative, so it is form A.

2. "Some students are attentive" is particular and affirmative, so it is form I.

3. "Students are never attentive" is universal and negative, so it is form E.

4. "Some students are not attentive" is particular and negative, so it is form O.

5. The stem describes a pair that cannot both be true but can both be false. That is exactly the contrary relation, and contrariety holds only between A and E.

6. Form A is proposition (a) and form E is proposition (c), so the code to select is (a) and (c).

Cross-check

Take a class in which some students are attentive and some are not. Then "Every student is attentive" is false and "Students are never attentive" is false as well, so that pair can indeed both be false. They cannot both be true, because "every" and "never" cannot describe the same non-empty class at the same time.

The table below contrasts all four offered codes.

Only A with E satisfies both conditions, so the answer is (a) and (c).