Outcomes Available for /A->B & /B->A Clarification pg. 315

[leslie7]

Hello,
I just want to clarify/confirm what I read on p.315, chp 5. for the given scenario /A-->B & /B-->A

In text "all that is indicated from the rule and its contrapositive is that A and will never both be unselected"...
but then says that...
"the rules never address what happens when either A or B is selected, only what happens when A or B is not selected.
Thus, when A is selected, B could be selected or B might not be selected.
Thus, when B is selected, A could be selected or B might not be selected."

So under the mentioned diagram there are three possible outcomes according to the textbook:
1. A is not selected and B is selected (makes sense)
2. B is not selected and A is selected (makes sense)
3. Both A and B are selected (makes sense since A --> maybe B , B --> maybe A)

but I'm wondering because of the wording above that states if A maybe B maybe not B and if B maybe A maybe not A ...could the the following two scenarios also be possible logical outcomes of which, could be added to the list of three to make it list of five possible outcomes?

A--->/B
B--->/A

only because we don't know what happens when A and what happens when B... does this make sense?

[Adam Tyson]

Thanks for the question, leslie! First things first, though, and that is that your original post had a typo in a quotation from the book, as follows:

In text "all that is indicated from the rule and its contrapositive is that A and will never both be selected"..

That last word should be UNselected, and I have corrected it in your original post. This isn't just being picky, but is an absolutely essential distinction. That rule, where the sufficient condition is negative and the necessary condition is positive, is a tricky, dangerous rule, and it means that you must always have at least one of the two variables and could perhaps have both. Putting them both out is impossible.

I'm not sure what you mean about adding those outcomes. If A is in, it is possible that B is not in - that's already covered by the "maybe B, maybe not" part of your analysis. This rule gives you just 3 possible outcomes - A is in and B is not, B is in and A is not, and A and B are both in. That's it, there is no 4th or 5th possible outcome.

Also, be careful not to treat this rule as if it is equivalent to A B, which could also be diagrammed with the Double-Not arrow: A B. This is NOT the same rule, because this rule does NOT allow you to select both A and B, and it DOES allow you to select neither of them (both are out, or unselected). Making that bad inference is the dangerous trap this type of rule can lead to if you aren't careful!