“An integer is either even or odd” is both exclusive (not both) and exhaustive (not neither). This is the haqiqiyyah form previously studied. Exclusivity permits inferring the negation of the other alternative from an affirmation; exhaustiveness permits inferring the other alternative from a denial.
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Exclusive and exhaustive alternatives
Types of Qiyas: Istithna’i and Iqtirani
“An integer is either even or odd” is both exclusive (not both) and exhaustive (not neither). This is the haqiqiyyah form previously studied. Exclusivity permits inferring the negation of the other alternative from an affirmation; exhaustiveness permits inferring the other alternative from a denial.