Contrapositive
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Definition
Given the statement [ilmath]A\implies B[/ilmath] (see implies) the contrapositive of this is: [ilmath]¬B\implies ¬A[/ilmath]
Proof:
| [ilmath]A[/ilmath] | [ilmath]B[/ilmath] | [ilmath]A\implies B[/ilmath] | [ilmath]¬A[/ilmath] | [ilmath]¬B[/ilmath] | [ilmath]¬B\implies ¬A[/ilmath] |
|---|---|---|---|---|---|
| T | T | T | T | ||
| T | T | T | T | ||
| T | T | ||||
| T | T | T | T |
So as can be seen:
- [math][A\implies B]\iff[¬B\implies ¬A][/math]
For example see Injection
TODO: Find reference
