Invalid argument:
If a number is divisible by 4, it is even.
But this number is even.
Therefore it is divisible by 4.
This does not follow: 6 is even but not divisible by 4. There can be many ways in which the consequent is true.
Thus “If A then B; B; therefore A” is invalid. The conditional presents A as sufficient for B, not as B’s only possible condition.
Opening interactive controls...
Exceptive Syllogism: Valid Inferences from Connected and Disjunctive Conditionals
Invalid argument:
If a number is divisible by 4, it is even.
But this number is even.
Therefore it is divisible by 4.
This does not follow: 6 is even but not divisible by 4. There can be many ways in which the consequent is true.
Thus “If A then B; B; therefore A” is invalid. The conditional presents A as sufficient for B, not as B’s only possible condition.