Modus Ponendo Tollens

Modus ponendo tollens (Latin: "mode that by affirming, denies") is a valid rule of inference for propositional logic, sometimes abbreviated MPT. It is closely related to modus ponens and modus tollens. It is usually described as having the form:

  1. Not both A and B
  2. A
  3. Therefore, not B

For example:

  1. Ann and Bill cannot both win the race.
  2. Ann won the race.
  3. Therefore, Bill cannot have won the race.

As E.J. Lemmon describes it:"Modus ponendo tollens is the principle that, if the negation of a conjunction holds and also one of its conjuncts, then the negation of its other conjunct holds."

In logic notation this can be represented as:

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