Contrapositive

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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

See also

References

  1. https://en.wikipedia.org/w/index.php?title=Contraposition&oldid=673682637