Hi,
This is a good question! What's happening is you are combining two different but related ideas, so let's break down how and why this works.
First, keep in mind that using abstract placeholders like with "A" and "B" makes it harder to see relationships initially. If we turn this into something more familiar like, "All apples are fruits (A
F), it's suddenly much easier to understand that "Some fruits are apples" (F some A) is true when you go in reverse, as well as that if you don't have any fruits then you don't have apples (
F A), is also true.
Second, to think about this more abstractly, the contrapositive is associated with conditional statements where you fully deny the necessary condition. When you have a statement like A
B, to enact the contrapositive you begin with the idea that "if no Bs occur." Once you add that new piece of information, that allows you to conclude that "no As occur," resulting in a diagram we show as:
B A. It's important to understand, though, that we added new information that "if B wasn't occurring" in order to allow that all to play out, and that our focus was on all the Bs not occurring.
In the Rules of Reversibility we are talking about, we are looking at what is
inherently true in a statement, and not adding in new information. So, let's start with that A
B statement again. What do we know just based on that alone? Looking at it from A's side, we know that every time we have an A, we also have a B there too. Okay, that seems obvious since all As are Bs. How about from B's side? Do we know that every time we have a B that we also have an A? No, and so the statement does NOT reverse to B
A. But we aren't quite done yet "going backward." We know that every time we have an A, then we have a B. So, if we stand on B's side, what we know is there are some Bs with As out there (and remember that these problems assume that As and Bs do exist). Is every B with A? No, we don't know that for sure (it's possible but not known 100%). So the fact that some AB combinations exist out there is what allows us to say that "going" backward that "some Bs are As."
Last, note that the contrapositive starts with "no Bs exist," where as out Reversibility discussion starts with "for the Bs that exist, how do they relate to A?" This is why there's no conflict here between the contrapositive and the reversibility ideas.
Please let me know if that helps. Thanks!
