Disjunctive syllogism

Disjunctive syllogism

Type	Rule of inference
Field	Propositional calculus
Statement	If ${\displaystyle P}$ is true or ${\displaystyle Q}$ is true and ${\displaystyle P}$ is false, then ${\displaystyle Q}$ is true.
Symbolic statement	${\displaystyle {\frac {P\lor Q,\neg P}{\therefore Q}}}$

In classical logic, disjunctive syllogism (historically known as modus tollendo ponens (MTP), Latin for "mode that affirms by denying") is a valid argument form which is a syllogism having a disjunctive statement for one of its premises.

An example in English:

1. I will choose soup or I will choose salad.
2. I will not choose soup.
3. Therefore, I will choose salad.