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. So, Bill cannot win 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:

1. $neg\; (A\; and\; B)$
2. $A$
3. $therefore\; neg\; B$

Other mathematical and logical symbols may be used to present this same form, such as:

1. ~(A • B)
2. A
3. $therefore$ ~B

It has also been described as having the following alternative forms:

References