Modus Ponendo Tollens

Proof Rule
The modus ponendo tollens is a valid deduction sequent in propositional logic: If two statements can not both be true, and one of them is true, it follows that the other one is not true.

It can be written:
 * $\displaystyle {\neg \left({p \land q}\right) \quad p \over \neg q} \textrm{MPT}_1 \qquad \text{or} \qquad {\neg \left({p \land q}\right) \quad q \over \neg p} \textrm{MPT}_2$

Variants
The following forms can be used as variants of this theorem:

Linguistic Note
Modus ponendo tollens is Latin for mode that by affirming, denies.

Also see
The following are related argument forms:
 * Modus Ponendo Ponens
 * Modus Tollendo Ponens
 * Modus Tollendo Tollens