If two propositions cannot both be false but may both be true, what is the…

Concept

In the traditional square of opposition, categorical propositions are classified as A, E, I, and O according to quantity and quality.

The four relations differ by which truth-value combinations they exclude: contraries exclude joint truth, subcontraries exclude joint falsity, contradictories exclude agreement in truth value, and subalternation expresses truth or falsity flow between corresponding universal and particular propositions.

Application

The condition says that the two propositions cannot both be false, while both may be true. This is exactly the defining truth-value pattern of a subcontrary pair.

Contrast and cross-check

• Contrary propositions cannot both be true, although both may be false; this reverses the condition in the stem.

• Subcontrary propositions cannot both be false, although both may be true; this reproduces both parts of the stated condition.

• Subalternation is the vertical relation between a universal proposition and its corresponding particular proposition, not a symmetric prohibition on joint falsity.

• Contradictory propositions must have opposite truth values, so they can be neither both true nor both false.

Therefore, the relation is sub-contrary.