Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping: Defined-Fixed, Balanced game.

The game scenario sets up a very simple Grouping arrangement:

PT52_Game#2_setup_diagram 1.png

The rules, however, are not quite as easy to handle. Although there are only four rules, they are each conditional, and the fourth rule is really three rules combined into one rule. Let us examine each rule in detail.

Rule #1

This rule can be diagrammed as:


JM LP


Of course, the contrapositive is in play as well, but because contrapositives should be second nature for simple conditional rules, we will not diagram the contrapositive.

Rule #2

This rule can be diagrammed as:

KM VO

This rule can also be diagrammed as:

KM VO

Thus, if one fails to occur, the other must occur.

Rule #3

This rule can be represented directly on the main diagram:

PT52_Game#2_setup_diagram 2.png

Rule #4

The final rule creates three negative grouping relationships:

PT52_Game#2_setup_diagram 3.png

This final rule creates a number of inferences when linked with the first two rules. For example, consider the first rule again:


JM LP


If this rule is in effect, K cannot be accompanied by M, and S cannot be accompanied by P. While that sufficient condition not-block is represented by the JK not-block above, the necessary condition not-block allows an inference to be drawn between J and S:


JM SP


In similar fashion, the following inferences can be drawn from combining the second and fourth rules:

KM TO


VO JM
(This inferences uses the contrapositive of the second rule)

Of course, because both inferences have negative sufficient and necessary conditions, the contrapositives should be examined:

TO KM


JM VO

As JM figures as the sufficient condition in one rule and one inference, a closer examination is warranted:

• When J is accompanied by M, then from the first rule, L must be accompanied by P, and from the inference above V must be accompanied by O. Because V must be accompanied by O, from the fourth rule, T cannot be accompanied by O, and thus according to the third rule, T must be accompanied by K.
  
  From the fourth rule, S cannot then be accompanied by P, and the only remaining spot for S is with O. K cannot be accompanied by M and must be accompanied by S. This information results in the following complete solution:

PT52_Game#2_setup_diagram 4.png

Because this solution is so powerful, do not expect to see J accompanied by M very often, if at all, in the game.

[Curtis1992]

Hello PowerScore,

I am a student of your online course and I just attempted the 2007 September LSAT . I am reviewing game two of the logic games section and I am completely confused on how to setup the game. I missed four out of the five questions and I am extremely confused as to what I did wrong so if I could get a setup for the game, maybe that could help.

Thanks
Curtis

[Amy Uecker]

Hi Curtis,

We posted the setup right above your question. Hope that helps, and please let us know if you have any additional questions!

[MeghanV]

Hello,
Could you please explain Rule #2 further? I understand the initial conditional diagram, but I'm not following the second way it is represented with the double not arrow.

[Daniel Stern]

Hi Meghan:

You asked about diagramming rule 2. The setup, posted at the start of this thread, suggests diagramming rule 2 as:

"Rule #2

This rule can be diagrammed as:
KM VO

This rule can also be diagrammed as:
KM VO

Thus, if one fails to occur, the other must occur."

The reason that we can use the Double Not Arrow is that it is a shorthand for the original rule and its contrapositive.

The original rule, again, was: KM VO

The contrapositive would be VO KM

Thus, putting K in the M group excludes V from the O group, and putting V in the O group excludes K from the M group.

The Double Not Arrow is just a shorthand way of expressing both of these ideas in one neat diagram.

KM VO

At a glance with that one diagram, I know that I can never have K in the M group at the same time that V is in the O group.

[mmhubbar]

Hi there,

Thank you so much for this explanation. I am having two problems specifically with this game, but also in general:

1. Is there something I should be looking for in a game that tells me I should make one/multiple templates? What rules guide you in making this decision? Is there generally a limit as to how many templates you can and should make? For example, I didn't even initially think in this scenario to make a template based off of Jm. And if I did, I would feel inclined to keep going and make more templates where possible.

2. I can see these inferences now, but get confused on how to make them. Why do you only change the necessary condition and not the sufficient condition when you make an inference? For example, you make an inference based on Rule 1 that Jm Lp you can make the inference that Jm ~Sp? Why do you not change Jm and only change the necessary condition, Lp, to ~Sp? Is that true for every instance where you make an inference based on a conditional statement?

[atierney]

Hello,

1. In general, you are looking for combinations of rules that are triggered by a primary "binary" rule (a rule that provides for only two outcomes). Ideally there is a single "binary" rule which you can map all the other rules on, giving you two templates. However, if there are multiple binary rules that are pretty significant to the set up, then you'll have to make more.

I generally tell my students to minimize the template-making-process, because I do think the patterns represented by the templates can be realized at a later stage of the game.

2. When you make inferences, they will be specific to the game, but generally, yes, the necessary condition is the condition that gives you the most meaningful information with respect to inferences and logically-valid conclusions. Here, our conclusions were based on the occurrence of the same sufficient condition, so we didn't change it in the diagram.

Let me know if you have further questions.