«هذا العدد إما زوج أو فرد»
This number is either even or odd.
This is a genuine disjunction, provided the subject is an integer. An integer cannot be both even and odd; nor can an integer be neither.
Exclusion of conjunction: even and odd cannot be jointly true.
Exclusion of omission: neither can be jointly false of an integer.
When both restrictions apply, the disjunction is genuine. The key is understanding both prohibitions, not merely repeating “either … or …”.
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Conditional Propositions: Connectives, Disjunctions and Their Main Kinds
«هذا العدد إما زوج أو فرد»
This number is either even or odd.
This is a genuine disjunction, provided the subject is an integer. An integer cannot be both even and odd; nor can an integer be neither.
Exclusion of conjunction: even and odd cannot be jointly true.
Exclusion of omission: neither can be jointly false of an integer.
When both restrictions apply, the disjunction is genuine. The key is understanding both prohibitions, not merely repeating “either … or …”.