For an integer:
Either even or odd.
It is not even.
Therefore it is odd.
Similarly:
Either even or odd.
It is not odd.
Therefore it is even.
These inferences rely on the fact that both alternatives cannot be false.
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Haqiqiyyah: denial establishes the other
Types of Qiyas: Istithna’i and Iqtirani
For an integer:
Either even or odd.
It is not even.
Therefore it is odd.
Similarly:
Either even or odd.
It is not odd.
Therefore it is even.
These inferences rely on the fact that both alternatives cannot be false.