Suppose: “If a number is divisible by 4, it is even.” We establish: “This number is not even.”
Antecedent: divisibility by 4.
Consequent: being even.
Exceptive premise: not even.
Therefore the number is not divisible by 4. This follows because any number divisible by 4 must be even.
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Exceptive Syllogism: Valid Inferences from Connected and Disjunctive Conditionals
Suppose: “If a number is divisible by 4, it is even.” We establish: “This number is not even.”
Antecedent: divisibility by 4.
Consequent: being even.
Exceptive premise: not even.
Therefore the number is not divisible by 4. This follows because any number divisible by 4 must be even.