Definition:Contradictory/Statements

Definition
Two statements $p$ and $q$ are said to be contradictory iff:
 * whenever $p$ is true, $q$ is false.

and:
 * whenever $q$ is true, $p$ is false.

Examples
The statements:
 * $1$ is a positive integer

and:
 * $1$ is not a positive integer

are contradictory.

Let the Universe of Discourse be fruit.

The statements:


 * Every mango is delicious.
 * There exists some mango that is not delicious.

are contradictory.

Also see

 * Definition:Contrary Statements
 * Definition:Subcontrary Statements
 * Definition:Square of Opposition


 * Definition:Contradiction


 * Principle of Non-Contradiction