Disjunction: This integer is even or odd.
Exceptive premise: But it is even.
Conclusion: Therefore it is not odd.
This works because an integer cannot be both even and odd. Accepting oddness as well would assert incompatible descriptions of the same number.
The inference uses the fact that both cannot be true together. It does not yet need the further claim that both cannot be false.
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Exceptive Syllogism: Valid Inferences from Connected and Disjunctive Conditionals
Disjunction: This integer is even or odd.
Exceptive premise: But it is even.
Conclusion: Therefore it is not odd.
This works because an integer cannot be both even and odd. Accepting oddness as well would assert incompatible descriptions of the same number.
The inference uses the fact that both cannot be true together. It does not yet need the further claim that both cannot be false.