For those non-logician zebras:
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.
e.g. TravelinMan is either a logician or an outstanding basketball official
TravelinMan is not a logician
Ergo, TravelinMan is an outstanding basketball official
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"You cant argue with logic"