Setup and Rule Diagrams

[Dave Killoran]

This game is also discussed in our Podcast: LSAT Podcast Episode 70: The May 2020 LSAT-Flex Logic Games Section

Setup and Rule Diagram Explanation

This is a Grouping: Defined-Fixed, Unbalanced: Underfunded game.

This game marks an increase in difficulty in this section, primarily because this game is not as clean as the prior two.


The game begins by introducing two separate variable sets:

• Six Meetings over two semesters: Fall: 1, 2, 3; and Spring: 1, 2, 3
  
  Five Cities: H, M, O, T, V

The six meetings might initially appear to have a sense of order, but as it turns out, the Fall/Spring Groups are key, and the Linear aspect is not relevant. Thus, those two semester groups can be selected as the base, and the diagram can be represented vertically or horizontally. Here's the setup appearing vertically:

• ___       ___
  
  ___       ___
  
  ___       ___
  Fall Spring

Note that, with only five city options and six spaces to fill, there is a 2-1-1-1-1 distribution of cities to spaces, and thus one of the cities will appear twice. Every other city will only appear once.

Let's take a moment to analyze the effects of that last point. Since every city must appear at least once, as soon as you know the the three cities in either semester (and thus that semester is filled), you automatically know two of the cities in the other semester. So, for example, let's say you knew that H, M, and O hosted in the fall; because T and V must also host, they must automatically be two of the cities in the spring. This is quite powerful when making hypotheticals in this game, and helps solve questions like #15 and #17 (where knowing 2 of the 3 then leads to a limited number of solutions).


With the base diagram in place, let's analyze the rules individually. Afterwards, we will dive into some of the interactions that lead to inferences:

• Rule #1: This is a conditional rule that establishes that when H hosts in the fall, then M must also host in the fall:
  
  
  H fall M fall
  
  
  The immediate thought for many students upon seeing a conditional rule in a game with two groups is to take the contrapositive, which would be:
  
  
  M fall H fall
  
  
  Of course, if this is a game with two groups, can't we apply two-value system thinking and change "not fall" into "spring" in the second diagram? Regrettably, no. This is not a two-value system game because you can have repeating variables, and thus, as my colleagues have jointly put it: "It's not a true two-value system, because there are three options for any given variable: (1) meeting in Fall (but NOT in Spring), (2) meeting in Spring (but NOT in Fall), and (3) meeting in both." And thus, "M being in the Spring does not prove H is in the Spring, because M could be in the Spring AND in the Fall."
  
  Understanding that this is not a true two-value game is critical to not being fooled into making false inferences!
  
  
  Rule #2: This rule is similar in form to the first rule, and can be diagrammed as:
  
  
  V spring T spring
  
  
  The contrapositive is:
  
  
  T spring V spring
  
  
  
  Rule #3: This rule reserves a space in each semester for M or V:
  
  
  • _____       _____
    
    _____       _____
    
    _M/V_ _M/V_
    Fall      Spring
  Note that these placements are not exclusive, and so M in one semester does not rule out V in that same semester, and vice versa. This is why each option is written as M/V (versus M/V and V/M, which would indicate the choice of one assigns the other). That indicates that this is a requirement that must be satisfied in each semester.

The rules are fairly straightforward to represent (aside from the tricky non-two-value system), and at this point in the game you can either proceed directly to the questions, or you can consider templates. Templates could be built around the variations on satisfying M and V rule, or on the variations of what occurs with placing the H and V from the first two rules. The former approach is fairly time-consuming and rather open, and thus doesn't strike us as the best use of time. The second approach is more useful since some of the templates fill in almost completely, and is a reasonable choice for those who take it. In this case, we chose not to use the Template approach, but it is defensible; it comes down to the approach you prefer.

[NR 2020]

Please post the remainder of the diagram, and inferences that can be drawn

[KelseyWoods]

Hi NR 2020!

Here's one possible setup with templates:

Screen Shot 2020-11-09 at 3.45.54 PM.png

Hope this helps!

Best,
Kelsey

[legalbeagle99]

Wouldn't the contrapositive of Hfall---->Mfall be Mspring---->Hspring

because M not fall means M spring since M has to go in either spring or fall and if it's not in fall then it must be in spring?

and

The contrapositive of Vspring------> TSpring be Tfall----->Vfall?

And T not Spring means T fall because if it's not in spring it must be in fall?

[Adam Tyson]

That's a good question, beagle, and an easy mistake to make, but it is a mistake in this case because this game does NOT set up a classic "two value system." My colleague Jeremy explains it well in this thread:

https://forum.powerscore.com/lsat/viewtopic.php?t=33059

Dave also talks about that in our podcast on this topic, found here:

https://blog.powerscore.com/lsat/lsat-p ... s-section/

(the discussion of the conditional rules in this game begins at around the 1:09:00 mark)

In short, M being in the Spring does not prove H is in the Spring, because M could be in the Spring AND in the Fall. One variable has to be in both seasons! So stick with the basic negation approach to the contrapositives here, as shown in our setup. If M is NOT in the Fall, H is also NOT in the Fall (and they would therefore both have to be in the Spring ONLY). Tricky stuff if you aren't careful about it!

[lsatstudying11]

Hello! I had a question about making templates based on the MV rule. While doing this game, I made the following 2 templates:

#1. M in F, V in S
F: [M] [ ] [ ]
S: [V] [ ] [ ] (and so T must also be in S)


#2. V in F, M in S
F: [V] [ ] [ ]
S: [M] [ ] [ ]


After reviewing, I wondered if the setup above was incomplete, and whether I would need to make 4 templates like this:

#1. M in F, V in S
F: [M] [ ] [ ]
S: [V] [ ] [ ] (and so T must also be in S)


#2. V in F, M in S
F: [V] [ ] [ ]
S: [M] [ ] [ ]

#3. M in F, M in S
F: [M] [ ] [ ]
S: [M] [ ] [ ]


#4, V in F, V in S
F: [V] [ ] [ ]
S: [V] [ ] [ ] (and so T must also be in S)


I guess I am wondering if the first 2-template setup would be incomplete? I figured that since I left open the possibility that I could tack an additional M or V in either group and since I knew that I had to include at least 1 of both M and V in the whole thing, these 2 templates were exhaustive. However, I am not sure if I am misunderstanding the MV rule. Thanks so much for your help!

[Adam Tyson]

Those first two templates would be incomplete in my view. Although you could say that they each include the idea that M or V could be in both seasons, that means they are almost useless, because you cannot take them further to make additional inferences. If you're going to do templates for this game, it would be better to do as you did later and consider those first two as being cases where each of M and V are only used once.

Templates are good when the game is restricted enough that there are only two or three possible starting positions, often based on a single rule or combination of rules that splits the game in two. I probably wouldn't do templates on this game myself, because there isn't anything about it that jumps out as having that kind of impact on the game. As much as I love doing templates, sometimes they just aren't worth the effort!

[ninluisa0]

Hello, I have a question regarding templates 2 and 3.
In template #2, the only repeating city is M. Why can't H also be a repeating city in the Spring? I thought it's because we placed H in the fall in this template and thus we can't put it as a repeating city in the Spring.
But in template #3, V is placed in the Spring AND it is also noted as a possible repeating city in the Fall.

[Adam Tyson]

In Template 2, ninluisa0, H cannot repeat because of the interaction of two rules that both affect M. First, that Template is based on H being in the Fall and V NOT being in the Spring. Here's what must happen in that case:

H in the Fall means M must also be in the Fall, because we have a rule that says exactly that.
V NOT being in the Spring means that M must be in the Spring, because we have a rule that requires either M or V in each season.

Thus, when H is in the Fall and V is NOT in the Spring, M is forced to be in both seasons, and every other variable must appear only once. If H were to repeat, we would either break one of those rules about M, or else we would have two variables repeating and one variable would be out of the game, which is not allowed by the 2-1-1-1-1 distribution.

V in the Spring relieves that pressure on M to be there, so the constraints are not quite the same, and V CAN be the one that repeats!

[emilyjmyer]

Hi!

I am having some trouble understanding the following rule:

"In each semester, either Montreal or Vancouver or both must host a meeting."

In my initial diagram I did put m/v for the fall and m/v for the spring. But what exactly does the rule mean? At first, I thought that this meant that the city that is put twice has to be M or V. Why is that not the case? Does this mean that there just cannot be a group without an M and V?

Thanks!