Grouping Games Rule Diagramming Drill #6

[Zarie Blackburn]

We recently received the following question from a student. An instructor will respond below. Thanks!

The solution to Question 6 of page 280’s Grouping Games Rule Diagramming Drill in Chapter 5 says that exactly one variable must be selected. Page 270 of the same chapter explaining the double-not rule says that they show that neither variable can be selected.

I don’t really understand why it can be used in the solution to Question 6 if it’s not true that, in that scenario, neither variable can be selected. I hope I’m not misunderstanding something obvious. Sorry to take up your time with this, but thank you for such a nice reply to my last email.

[Dave Killoran]

Hi,

On page 270 we have:

• If R is selected, then H is not selected.
  
  Diagram:
  R H

This rule is presented in isolation (which is key here), and the representation captures three solutions (one or the other, or neither).

On page 280, #6 the situation is different, and now includes an actual diagram of available spaces. On that diagram, we show that one of of F or G must be shown (thus eliminating the neither outcome). We still want to show that both can't be selected, and the F G diagram allows us to show that impossibility. That diagram, when combined with the representation on the Group of 5 sections, allows us to understand that one and exactly one of the two must be present.

You could also have shown the rule as follows:

• F G
  and
  F G

But showing F/G in the diagram is more effective since it captures the at least one (F G) relationship far more powerfully in a visual sense.

The takeaway here though is that using ideas in combination will change what you know, and you can use different tools to represent what is occurring. Both double-not arrow rules overlap, which is why our representation have some overlap on pages 270 and 280.

Thanks for the questions and please let me know if that helps!

[sim.LSAT]

Hi,

I am currently working on the Grouping Games Rule Diagramming Drill pg 301 (LG Bible 2020). I have a question regarding question 6.

The answer states that the diagram should be F G. However, this allows for the possibility of both F and G being "out," which according to the question would be wrong since either F or G must be selected. So, shouldn't the diagram be:
~F G
~G F
and since "not both," we also need to include the following diagram.
F ~g
G ~f

This would ensure that either F or G is selected and prevents both F and G being "out." Can someone please clarify why it has been diagrammed as a double-not arrow rather than as above?


Thank you!

[Dave Killoran]

Hi Sim,

Thanks for the question!

It was done because since only one variable is selected as being out in this drill (note that is says "non-selection" not "non-selections"), and thus it can never physically occur that both F and G are out, hence an additional diagram saying that wasn't necessary There is no harm in showing it, however, other than a few extra seconds.

The good news here is that you clearly understand the range of possibilities, and that's the real lesson underneath all of this so congrats there

Thanks!

[Zarie Blackburn]

We recently received the following question from a student. An instructor will respond below. Thanks!

In chapter 5, page 303, I think the answer key is incorrect for question 6:

The double not arrow between F and G would mean that there are three possible scenarios:
1. F occurs and G doesn’t
2. G occurs and F doesn’t
3. They both don’t occur

According to the rule, one MUST occur, so the double not arrow for scenario three is incorrect.

[Dave Killoran]

In chapter 5, page 303, I think the answer key is incorrect for question 6:

The double not arrow between F and G would mean that there are three possible scenarios:
1. F occurs and G doesn’t
2. G occurs and F doesn’t
3. They both don’t occur

According to the rule, one MUST occur, so the double not arrow for scenario three is incorrect.

So, the "not both" segment of the rule does indeed eliminate the chance that F and G are both selected, so it is appropriate to use that diagram. In other words, "Not both of F and G" is in fact F G. But, there's a second part to this, which is that "Either F or G is selected." That's what knocks out the third scenario, and it's also what forces the outcome to be where one is selected and one is not selected, which is then how the rule is diagrammed on the diagram (and the note in the text reference that "exactly one" idea).

Thanks!

[Matteod]

So just to clarify, the reason that double-not-arrow diagram works is because of the ‘either F or G’ aspect of the rule - meaning, we are implicitly suppose to avoid the third scenario I mentioned (both F and G don’t occur) because of this specification. Wouldn’t it be more useful to use the following diagram (given there is no implicit intuition based on the rules and encompasses everything necessary):

F ~G
G ~F

~F G
~G F

This way, the third scenario would never even be considered? Maybe I am overthinking this.

Best,
Matteo

[Dave Killoran]

So just to clarify, the reason that double-not-arrow diagram works is because of the ‘either F or G’ aspect of the rule - meaning, we are implicitly suppose to avoid the third scenario I mentioned (both F and G don’t occur) because of this specification.

Yes! That's the meaning of either/or in an isolated context: "at least one"

Wouldn’t it be more useful to use the following diagram (given there is no implicit intuition based on the rules and encompasses everything necessary):

F ~G
G ~F

~F G
~G F

This way, the third scenario would never even be considered? Maybe I am overthinking this.

Best,
Matteo

That works 100%, but we bypassed it with the F/G notation in the diagram.

Thanks!