وإن كانت منفصلة حقيقية فاستثناء عين أحدهما ينتج نقيض الآخر وبالعكس
If the conditional is a true disjunction, asserting either side yields the negation of the other, and conversely.
For example, an integer is either even or odd. It cannot be both, nor can it be neither.
Thus affirming evenness denies oddness, while denying evenness establishes oddness. The corresponding inferences also work from the other side.
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Exceptive Syllogism: Valid Inferences from Connected and Disjunctive Conditionals
وإن كانت منفصلة حقيقية فاستثناء عين أحدهما ينتج نقيض الآخر وبالعكس
If the conditional is a true disjunction, asserting either side yields the negation of the other, and conversely.
For example, an integer is either even or odd. It cannot be both, nor can it be neither.
Thus affirming evenness denies oddness, while denying evenness establishes oddness. The corresponding inferences also work from the other side.