"All birds migrate south in winter. The monarch butterfly is not a bird. Therefore, the monarch butterfly does not migrate south in winter."
Apply group 1 because of "All" indicator, so the sufficient condition is A = Birds, and the necessary is B = (migrate south in winter) to get Lawgic rule of A -> B. Otherwise stated using if conditional, this is "If something is a bird, then it migrates south in the winter."
Contrapositive would then be !B -> !A, or "if something does not migrate south in the winter, then it is not a bird."
Then we have "The monarch butterfly is not a bird," which maps onto the necessary condition of the contrapositive form ("...it is not a bird."). We cannot make any kind of assumption from this, as a necessary condition being met does not imply anything about the existence of any corresponding sufficient condition being met, thus the conclusion that "the monarch butterfly does not migrate south in winter" is not valid.
This makes sense, however the following example of the text does not. Changing the modifier from "all" to "only" switches the conditions that are presented as being sufficient and necessary. The "only" modifies the things that fly south in the winter to be birds and birds alone, meaning birds are transformed into the necessary condition and things that fly south in the winter into the sufficient. This gives us B -> A (using the same variable mapping as above). When the end of the problem states "The only problem is that you made up your own premise B → A. The actual premise is A → B. You confused sufficiency for necessity," it ignores that the new wording of the premise has actually flipped the sufficient and necessary conditions, and therefore the reasoning of the argument is valid. See below:
"Only birds migrate south in winter. The monarch butterfly is not a bird. Therefore, the monarch butterfly does not migrate south in winter."
Apply group 2 because of "Only" indicator, so "only" indicates necessary condition A = Birds, and makes B = "migrate south in winter" the sufficient. This gives the rule:
B -> A, otherwise stated using if conditional as "if something migrates south in the winter, then it is a bird."
The contrapositive of this would then be:
!A -> !B, or "if something is not a bird, then it does not migrate south in winter." Here, "The monarch butterfly is not a bird" clause satisfies the sufficient condition of the contrapositive, meaning we can indeed draw a conclusion that it does also fit the necessary, being that it does not fly south in winter.
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"All birds migrate south in winter. The monarch butterfly is not a bird. Therefore, the monarch butterfly does not migrate south in winter."
Apply group 1 because of "All" indicator, so the sufficient condition is A = Birds, and the necessary is B = (migrate south in winter) to get Lawgic rule of A -> B. Otherwise stated using if conditional, this is "If something is a bird, then it migrates south in the winter."
Contrapositive would then be !B -> !A, or "if something does not migrate south in the winter, then it is not a bird."
Then we have "The monarch butterfly is not a bird," which maps onto the necessary condition of the contrapositive form ("...it is not a bird."). We cannot make any kind of assumption from this, as a necessary condition being met does not imply anything about the existence of any corresponding sufficient condition being met, thus the conclusion that "the monarch butterfly does not migrate south in winter" is not valid.
This makes sense, however the following example of the text does not. Changing the modifier from "all" to "only" switches the conditions that are presented as being sufficient and necessary. The "only" modifies the things that fly south in the winter to be birds and birds alone, meaning birds are transformed into the necessary condition and things that fly south in the winter into the sufficient. This gives us B -> A (using the same variable mapping as above). When the end of the problem states "The only problem is that you made up your own premise B → A. The actual premise is A → B. You confused sufficiency for necessity," it ignores that the new wording of the premise has actually flipped the sufficient and necessary conditions, and therefore the reasoning of the argument is valid. See below:
"Only birds migrate south in winter. The monarch butterfly is not a bird. Therefore, the monarch butterfly does not migrate south in winter."
Apply group 2 because of "Only" indicator, so "only" indicates necessary condition A = Birds, and makes B = "migrate south in winter" the sufficient. This gives the rule:
B -> A, otherwise stated using if conditional as "if something migrates south in the winter, then it is a bird."
The contrapositive of this would then be:
!A -> !B, or "if something is not a bird, then it does not migrate south in winter." Here, "The monarch butterfly is not a bird" clause satisfies the sufficient condition of the contrapositive, meaning we can indeed draw a conclusion that it does also fit the necessary, being that it does not fly south in winter.