- Either P or Q.
- Not P.
- Therefore, Q.
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.