Definition:Contradictory Statements

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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


Sources