Grouping Games Rule Diagramming Drill - pg 301 Q 6 <--/-->

[leslie7]

I understand the difference between these two statements but I am unsure about what the double-not arrow represents if it is being utilized for what appears to me to be two different meanings, if I am going by the description of the text book.

According to p. 290 if we have a double not arrow (for ex. R<--/-->H) it only prohibits one scenario where R and H can be selected together or cannot occur together (makes sense to me). This also implies that these scenarios can occur:
R and not H, H and not R or not both (not H and not R)

However, in q 6 pg 301 the scenario is
Either F or G but not both, must be selected , represented with a double not arrow but I take to issue here with the second portion of the clause that says "one must be selected" which is correctly diagramed in the exercise answer key with F/G under selected and F/G under not selected (this scenario makes sense to me).

But my question is how do we define the double not arrow? Does it in principle, based on its definition always imply that the "not both" scenario is possible? and maybe is the placing of F/G in the in and F/G in the out group just an "addendum" or "adjustment" to the double not arrow to read that one of them "must be selected"

I think my question might seem a little scattered but in summary I am understanding the difference between If R is selected then H is not selected versus Either F or G, but not both, must be selected but I'm not at its understanding how if the double not arrow has one meaning how it can be applied to the two different scenarios where (one accepts a not both scenario and the other doesn't).

I hope I'm somehow clear - any clarification would greatly help. It's possible I'm not fully grasping its definition or perhaps the double not arrow can be inclusive of more than one meaning when expanded upon with more diagraming?

Thanks so much.

[Adam Tyson]

The Double-Not Arrow always means that the two things on either side of the arrow cannot both occur, leslie7 - you've got that right. In a scenario where you must have one or the other but not both, the Double-Not arrow will capture only half of the rule, the part that says "not both." You still need to do some extra work to capture the idea that one of them must occur, and there are a few ways to do that, including the one described in the book of putting a split option with one variable in the In group and the other in the Out group. That could actually cover the entire rule, making the Double-Not arrow superfluous.

Another option is to do a second version of the Double-Not arrow, this time with both variables negated, like this:

F G

While this may be a little confusing at first look, it is still a standard Double-Not arrow in action. This time it is telling us that "F out" and "G out" cannot both occur, which means that at least one of them must be in the In group.

My first choice in a game like this, where everything is either in or else out, and where there is a pair of variables for which one has to be in and the other has to be out, is to skip the use of the arrows and just use the split option approach. But the arrows are a good backup and reminder that might help some students to avoid certain errors as they move through the questions, so do whatever works for you.

I hope that clear things up!