Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping: Undefined game.

The game scenario establishes that there are six dancers, but an exact number of dancers on the stage is not given, making this an Undefined game. The dancers fall into two groups—“on stage” and “off stage”—and the choice is yours to show both groups, or just to show the “on stage” group in your main diagram. As stated elsewhere, we typically show just the “in” group of variables, which in this case would be the “on stage” group.

Thus, prior to examining the rules, we have the following basic setup:

PT54-Jun2008_LGE-G1_srd1.png

Rules #1 and #2. These rules are best examined together because they both address the relationship of J and L.

The first rule establishes that when J is on stage, then L is off stage:

PT54-Jun2008_LGE-G1_srd2.png

As this rule means that when one of J or L is on stage, the other must be off stage, this rule is better diagrammed as:

PT54-Jun2008_LGE-G1_srd3.png

Essentially, then, J and L can never both be on stage at the same time.

The second rule indicates that when L is off stage, then J must be on stage:

PT54-Jun2008_LGE-G1_srd4.png

As discussed elsewhere, this is one of the trickiest rules to encounter in Logic Games. When L is not on stage, J must be on stage. Via the contrapositive, when J is not on stage, then L must be on stage. Thus, whenever J or L is off stage, the other must be on stage. This means the two can never both be off stage at the same time, which can be represented as:

PT54-Jun2008_LGE-G1_srd5.png

The first rule indicates that both J and L cannot be on stage at the same time, and the second rule indicates that J and L cannot both be off stage at the same time. Thus, when the two rules are combined, we can infer that one of J and L is always on stage, and the other is always off stage. With this information, we can modify our main diagram to appear as:

PT54-Jun2008_LGE-G1_srd6.png

Rule #3. The third rule can initially be diagrammed as:

PT54-Jun2008_LGE-G1_srd7.png

However, the contrapositive of this rule is more helpful:

PT54-Jun2008_LGE-G1_srd8.png

Thus, when J is on stage, then F must also be on stage. Of course, if F is not on stage, J is not on stage, and from the first two rules we can infer that L would then have to be on stage:

PT54-Jun2008_LGE-G1_srd9.png

Rule #4. This rule establishes that if any of the women are on stage, then G is also on stage:

PT54-Jun2008_LGE-G1_srd10.png

By itself, this rule would force you to track when a woman is on stage. However, from the first two rules we have already established that either J or L is always on stage. Because both J and L are women, we can thus infer that G must always be on the stage.

The information above leads to the final diagram for this game:

PT54-Jun2008_LGE-G1_srd11.png

[LSAT2018]

I was just wondering if my representation of the first and second rules are correct:
Jaclyn → Lorena (Contrapositive: Lorena → Jaclyn)
Lorena → Jaclyn (Contrapositive: Jaclyn → Lorena)

So the first rule indicates that both can't be on stage, and the second rule indicates that at least one is on stage (since both can't be on stage as stated in the first rule). So this is a bi-conditional in the form of A or B, but not both (A or B but not otherwise) which means either A is selected without B, or else B is selected without A:

Jaclyn ↔ Lorena
Jaclyn ↔ Lorena


Would this be right? So Jaclyn or Lorena is always in, and Jaclyn or Lorena is always out.

[Brook Miscoski]

LSAT2018,

You could do the rules as follows:

1. J L
2. -L -J

Where a positive is onstage and a negative (or cross-through) is offstage.

I don't see any value in talking about biconditionals. It's certainly not an "if and only if" statement.

Where the value is, is in recognizing that either J is onstage or J is offstage. The first rule establishes that J and L can't be onstage together, the second rule establishes that J and L can't be offstage together. That means that one of them is onstage and the other one is offstage in every valid scenario. Therefore, your final inference is correct.

[ncolicci11]

Hi Powerscore,

Could you walk through the setup for this game?

Thanks!!

[Adam Tyson]

I'll happily try, ncolicci11, but I'm not (yet) great at creating the diagrams in this format, so you'll have to follow my steps and draw them out for now.

As discussed above in this thread, the first two rules tell us that at least one of J and L is always on stage, and at least one of them is always off stage. This allows us to infer that at all times, one of those two is on and the other is off.

The third rule is a simple enough conditional statement that looks like this when diagrammed (including the contrapositive, which may be easier to deal with):

F J
J F

The last rule establishes that if any of J, K, of L is on stage, G must also be. Rather than diagram that as the conditional statement that it is, let's go ahead and combine it with the second rule, which required that there is always at least one of J or L is on stage. This means that G must always be on stage!

Our "in" group (those that are on stage) must therefore consist of G and exactly one of J or L, and could include others. H is a random here and so can be on or off with no restrictions. K, although not technically random because it is part of the last rule, is now completely free to come or go with no effect either way.

I would not do templates for this game, but for the sake of this explanation I will show two possible outcomes:

1. G and L are onstage. This forces J offstage. F, H, and K can be on or off in any combination, a very flexible situation.

2. G and J are onstage. This forces L offstage and, per the third rule, F must be onstage. H and K can be on or off in any combo.

Take it from there and have fun!

[ncolicci11]

Hi Adam!

Thank you- very much appreciated. About inferences in general, is there a certain method you prefer to follow that helps identify when you can no longer pull inferences? I feel that I often am looking to hard for inferences that do not exist...

Thanks again!

[Adam Tyson]

I'll share our "microwave popcorn" analogy - when popping slows to 2-3 seconds between pops, hit the Stop button and get the bag out of the microwave, even if that means some unpopped kernels in the bottom of the bag. When the inferences slow down, and it's taking a few seconds to see what's next, stop trying so hard and get to the questions. It's okay to miss an inference or two, but it is NOT okay to make no effort at finding any. Scoop up any obvious ones, search a little for a couple more, and then get on with the business at hand.

[pwfquestions]

Why is the second version of rule three better than the negative version?
Why is there no contrapositive listed of rule 4?

Thanks

[Robert Carroll]

pwfquestions,

Why is the second version of rule three better than the negative version?
Why is there no contrapositive listed of rule 4?

Thanks

Because a conditional using affirmative statements is usually easier to deal with than one using negatives.

A contrapositive of the fourth rule would be pointless, since G is always on stage.

Robert Carroll

[Mmjd12]

Regarding the inference: F J L

I diagrammed it as F L

And it’s contra positive, L F

Is this incorrect or does it materially mean the same thing?