Definition:Contradictory/Statements

Definition

Two statements $p$ and $q$ are said to be contradictory if and only if:

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

Sources

• 1946: Alfred Tarski: Introduction to Logic and to the Methodology of Deductive Sciences (2nd ed.) ... (previous) ... (next): $\S \text{II}.7$: Sentential Calculus
• 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): Chapter $2$: The Propositional Calculus $2$: $3$ Truth-Tables: $\text {(vi)}$
• 1995: Merrilee H. Salmon: Introduction to Logic and Critical Thinking: $\S 10.2$