Which pair are contraries?

• A. A and E statements
• B. I and O statements
• C. A and I statements
• D. E and O statements

Answer: (A)

Contraries arise between universal propositions. A universal affirmative says all members of the subject class are in the predicate class, while a universal negative says no members are. These two cannot both be true, but they can both be false. For example, “All swans are white” and “No swans are white” cannot both hold, but it could be that some swans are white and some are not, making both statements false. So the pair of universal forms—All S are P and No S are P—are contraries. The other pairings mix universal with particular or pair the two particulars, which follow different relationships (subalternation or subcontraries) and are not contraries.