“Or” joins clauses into one compound proposition. It does not establish the truth of each clause separately.
For example:
This integer is either even or odd.
The compound claim can be true without identifying which alternative holds. More information—such as the number itself or exclusion of one alternative—is required to affirm a particular side.
In disjunctive syllogisms, a valid conclusion preserves the appropriate alternative structure instead of asserting an arbitrary disjunct.
Opening interactive controls...
Conjunctive Syllogisms with Conditional Propositions
“Or” joins clauses into one compound proposition. It does not establish the truth of each clause separately.
For example:
This integer is either even or odd.
The compound claim can be true without identifying which alternative holds. More information—such as the number itself or exclusion of one alternative—is required to affirm a particular side.
In disjunctive syllogisms, a valid conclusion preserves the appropriate alternative structure instead of asserting an arbitrary disjunct.