Contradiction

Contraries

A and E propositions. Contraries cannot both be true, but they can both be false. To refute an A or E proposition, you do not need to prove its contrary, only its contradictory.

Subcontraries

I and O propositions. Subcontraries can both be true.

Opposition

The relation between any two propositions that have the same subject and the same predicate but differ in quality or quantity or both.

Contradiction

Two propositions contradict each other only when the truth of either one necessarily means the falsity of the other, and the falsity of either one necessarily means the truth of the other. And this happens only between propositions that (a) have the same subject and predicate (b) and differ both in quantity and quality. Of two contradictories, if one is true the other is false and if one is false the other is true.

Subalternation

The relationship between opposed A and I and E and O propositions. The propositions are called subalternates.