Disjunctive syllogism

A disjunctive syllogism is one valid, simple argument form:

Either P or Q.

Not P.

Therefore, Q.

In logical operator notation:

where represents the logical assertion.

Roughly, we are told that it has to be one or the other that is true; then we are told that it is not the one that is true; so we infer that it has to be the other that is true. The reason this is called "disjunctive syllogism" is that, first, it is a syllogism--a three-step argument--and second, it contains a disjunction, which means simply an "or" statement. "Either P or Q" is a disjunction; P and Q are called the statement's disjuncts.

Here is an example:

Either I will choose soup or I will choose salad.

I will not choose soup.

Therefore, I will choose salad.

Here is another example:

Either the Browns win or the Bengals win.

The Browns do not win.

Therefore, the Bengals win.