# Contrapositive

From Maths

## Definition

Given the statement [ilmath]A\implies B[/ilmath] (see implies) the *contrapositive* of this is^{[1]}: [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 the definition of: Injection