Definition:Contrary Statements

Definition
Two statements are said to be contrary if they can both be false, but they cannot both be true.

Example
Let the Universe of Discourse be fruit.

The statements:


 * Every mango is delicious.
 * Every mango is not delicious.

are contrary.

Also see

 * Definition:Logical NAND


 * Definition:Categorical Statement
 * Definition:Contradictory Statements
 * Definition:Subcontrary Statements
 * Definition:Square of Opposition


 * Principle of Non-Contradiction

Linguistic Note
In this context, the word contrary is pronounced with the stress on the first syllable: con-tra-ry.

There is a different usage of contrary which means, of a person, perversely inclined to disagree or to do the opposite of what is expected or desired. In this context, the stress is on the second syllable: con-tra-ry, making it rhyme, conveniently, with Mary, hence the children's nursery rhyme:
 * Mary, Mary, quite contrary
 * How does your garden grow?
 * With silver bells and cockle shells
 * And pretty maids all in a row.

which, it has been suggested, may have been written as a social satire on the reign of either of the 17th-century queens in Britain: Mary, Queen of Scots or the thoroughly reprehensibly evil Mary I of England.