Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

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

The game scenario establishes that eight people—three adults and five children—will be assigned to two groups of four people each:

PT19-Jun 1996 LGE-G3_srd1.png

Because there are only two groups, and every variable must be in one of the two groups, the groups form a two-value system, which plays a major role in the game.

The first rule establishes that each boat is assigned at least one adult, so reserve a space in each boat for F, G, and H:

PT19-Jun 1996 LGE-G3_srd2.png

The second rule is conditional:

PT19-Jun 1996 LGE-G3_srd3.png

Of course, because the game is a two-value system, when we take the contrapositive, we can convert the negatives into positives by changing the boat number (if G is not in boat 2, then G must be in boat 1, etc):

PT19-Jun 1996 LGE-G3_srd4.png

Note that this rule (and its contrapositive) does not imply that F and G are always in the same boat. For example, G could be in boat 2 and F could be in boat 1.

The first two rules can be combined to create two inferences. When F is assigned to boat 2, G is assigned to boat 2, and because there must be an adult in each boat, H must then be assigned to boat 1.

PT19-Jun 1996 LGE-G3_srd5.png

Similarly, using the contrapositive of the second rule, when G is assigned to boat 1, F is assigned to boat 1, and then H must be assigned to boat 2:

PT19-Jun 1996 LGE-G3_srd6.png

The contrapositive of these last two inferences, again accounting for the two-value system:

PT19-Jun 1996 LGE-G3_srd7.png

The third rule is similar to the second:

PT19-Jun 1996 LGE-G3_srd8.png

As always, make note of the contrapositive in any two-value system game:

PT19-Jun 1996 LGE-G3_srd9.png

Note that this rule (and its contrapositive) does not imply that V and W are always in different boats. For example, V could be in boat 2 and W could be in boat 2.

The fourth and final rule indicates that X and Z are in different boats. The best diagram for this rule is to place X/Z dual options on the main diagram, while also noting that Y is a random (while H is not directly named, H is covered under the actions of the first rule):

PT19-Jun 1996 LGE-G3_srd10.png

Combining all of the prior information leads to the final setup:

PT19-Jun 1996 LGE-G3_srd11.png

[ellenb]

Dear Powerscore,

So, I have done this game and when I looked at the explanation in one of the Powerscore's Setup Guides, I found a partial explanation. And only the answers to some questions. That is why I wanted to make sure I understood the answers to the other ones.

1) Can we have a horizontal setup? ( I was just curious why they chose in the explanations a vertical set-up for this game)
Ex: 1_ _ _ _
2_ _ _ _


Thanks!

[Dave Killoran]

Hi Ellen,

Hmm, I'm thinking you must be referring to the Ultimate Setups Guide. That book went out of print a number of years ago, and we replaced that book with the LSAT Logic Games Setups Encyclopedias (http://www.powerscore.com/lsat/content_ ... ions.cfm#2). Those books have comprehensive explanations for each setup and complete explanations for every single question.

In response to the horizontal/vertical question, that game is actually set up in a horizontal fashion, depending on how you look at it. The Base is the boat numbers--1 and 2--and those are set up horizontally. The game just look vertical because there are four spaces above each number (think about how different it would look if there was just one space above each number--then it would look more horizontal).

However, as we note in our discussions of Linear games, you can set up almost any game in a horizontal or vertical fashion, so if you prefer to have the boat number on the side instead of the bottom, then definitely do that! It's functionally identical and won't cause a problem at all in this game.

Please let me know if that helps. Thanks!

[ellenb]

Thanks Dave,

It really helps to know that there is an updated version .

Best,

Ellen

[ChicaRosa]

When I did this game I was very confused about diagramming the rules and understanding the inferences from the rules. I understood that it was a Grouping Game with equal amount of variables.

Here's how I diagrammed and wrote the rules

----- = adults
= children

1: ----- ----- 1: -----

2: ----- 2: ----- -----


2) F2 G2, contrapositive: G1 F1

3) V1 W2, contrapositive: W1 V2

4) X Z


Did I diagram the rules right?


How would question 17 allow V and W to be together in the same boat if rule 3 states otherwise?

Also, does rule 1 mean that F and G have to go in the same boat leaving H alone in each of the scenarios?

Thank You!

[Nikki Siclunov]

Hi ChicaRosa,

Thanks for your question. Your basic setup for this game is fine; however, I'm afraid you're misinterpreting the implications of the conditional rules we're dealing with.

For instance, V and W can easily be in the same boat as each other, as long as that boat is not boat #1. If either of them is in boat #1, the rule clearly requires the other one to be in boat #2. But what if W is in 2? To conclude anything about V would be a Mistaken Reversal of the original rule. Likewise, what if V is in 2? To conclude anything about W would be a Mistaken Negation. Consequently, V and W can easily be in the same boat as each other, as long as it's boat #2.

The same reasoning applies to F and G. If F is in 2, then yes - F and G must be in the same boat as each other (boat #2), leaving H to be in boat #1. Likewise, if G is in 1, then F and G must both be in 1 (leaving H to be in boat #2). However, does not tell us what must be true if either F is in boat #1, or else if G is in boat #2. Therefore, F and G can be in two separate boats, as long as F is not in 2 (i.e. in 1), and G is not in 1 (i.e. in 2).

Hope this clears it up! Let me know if you have any other questions.

Thanks,

[ChicaRosa]

Hi ChicaRosa,

Thanks for your question. Your basic setup for this game is fine; however, I'm afraid you're misinterpreting the implications of the conditional rules we're dealing with.

For instance, V and W can easily be in the same boat as each other, as long as that boat is not boat #1. If either of them is in boat #1, the rule clearly requires the other one to be in boat #2. But what if W is in 2? To conclude anything about V would be a Mistaken Reversal of the original rule. Likewise, what if V is in 2? To conclude anything about W would be a Mistaken Negation. Consequently, V and W can easily be in the same boat as each other, as long as it's boat #2.

The same reasoning applies to F and G. If F is in 2, then yes - F and G must be in the same boat as each other (boat #2), leaving H to be in boat #1. Likewise, if G is in 1, then F and G must both be in 1 (leaving H to be in boat #2). However, does not tell us what must be true if either F is in boat #1, or else if G is in boat #2. Therefore, F and G can be in two separate boats, as long as F is not in 2 (i.e. in 1), and G is not in 1 (i.e. in 2).

Hope this clears it up! Let me know if you have any other questions.

Thanks,

Hi Ms. Siclunov,

If were to diagram the mistaken reversal of W being in boat 2 would it be like this: W2 V1?

I am confused but how would it be a Mistaken Negation to conclude anything about W, if V is in boat 2 and how would the diagram look like? I thought it would be a Mistaken Reversal because if someone is assuming that the necessary condition brings the sufficient condition .

Besides that I think your explanation is very helpful . The bottom line is that the necessary condition doesn't rely on the sufficient condition for an event to happen and that the sufficient condition needs the necessary condition to make the event happen.

Thank you very much for taking the time to help me with this question!

[Nikki Siclunov]

Hi ChicaRosa,

Thanks for the follow-up. The original rule is stated as follows:

• V1 W2
  W1 V2 (contrapositive)

As you will notice, the Mistaken Reversal of the original rule (W2 V1) can also be understood as a Mistaken Negation of the contrapositive. Likewise, the Mistaken Reversal of the contrapositive (V2 W1) is actually the Mistaken Negation of the original rule. Ultimately, the MN and MR are contrapositives of each other: they are both unwarranted inferences from the same conditional rule. The precision with which we label the incorrect inference is not nearly as important as knowing why the inference is incorrect!

Hope this helps!!

Nikki

[LSAT2018]

While forming the setup, I was able to find the contrapositives of the two conditional reasoning statements:
F (Group 2) → G (Group 2)
G (Group 1) → F (Group 1)

V (Group 1) → W (Group 2)
W (Group 1) → V (Group 2)

Were there other inferences for the entire setup that I might have missed?

[Shannon Parker]

While forming the setup, I was able to find the contrapositives of the two conditional reasoning statements:
F (Group 2) → G (Group 2)
G (Group 1) → F (Group 1)

V (Group 1) → W (Group 2)
W (Group 1) → V (Group 2)

Were there other inferences for the entire setup that I might have missed?

The only other inferences are based on the rule that X and Z are assigned to different boats. So X(group 1)--->Z(group 2), Z(group 1)--->X(group 2).

Keep up the good work.
Shannon