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

Concept

Traditional categorical logic classifies propositions as A, E, I, and O: universal affirmative, universal negative, particular affirmative, and particular negative.

On the traditional square of opposition, I and O propositions are subcontraries: both may be true, but they cannot both be false, under the traditional existential interpretation.

Application

1. Proposition (a), ‘Some priests are cunning,’ is a particular affirmative (I) proposition.

2. Proposition (b), ‘No priest is cunning,’ is a universal negative (E) proposition.

3. Proposition (c), ‘All priests are cunning,’ is a universal affirmative (A) proposition.

4. Proposition (d), ‘Some priests are not cunning,’ is a particular negative (O) proposition.

5. The required relation is subcontrariety, so the pair must contain the I and O forms: (a) and (d).

Cross-check and contrast

• The pair (a) and (b) combines I and E, which are contradictories: they cannot both be true and cannot both be false.

• The pair (c) and (d) combines A and O, which are contradictories: they cannot both be true and cannot both be false.

• The pair (a) and (c) combines I and A in subalternation, not the required subcontrary relation.

• The pair (a) and (d) combines I and O. A population containing both cunning and non-cunning priests makes both statements true; making both false would require the incompatible A and E forms.

Therefore, the required propositions are (a) and (d).