Setup and Rule Diagrams

[lsatdaynnight]

I am having a difficult time incorporating the contrapositive of Rule 2 while making different scenarios. Would it be possible to please explain how to set up this game? I reviewed the previous explanations but was not able to follow the process so, if possible, would appreciate a detailed explanation. Thank you very much!

[Adam Tyson]

I'll give it a try, lsatdaynnight!

First, Rule 2 tells us that if G is before T, then R and S must also be before T. I won't be able to draw that in this forum exactly as I would on paper, but it's basically this:

G T R and S T

When you do the contrapositive, you reverse the order and change the "and" that is in the necessary condition to an "or" in the sufficient condition, so you get this:

(T R OR T S) T G

(Switching the order is "negating" the conditions here since there can be no ties. T can only be before G or else after G.)

When we build templates in this game around the last rule, we get two starting positions. Either H is before both S and T or else it is after both S and T. H can never be between them.

If we start with S and T both before H, and we couple that with the first rule that H is always before R, we get:

S and T H R

This triggers the contrapositive of the second rule, because T is before R. Thus, in this template, T must also be before G. Either S or T is first, and G could be second (after T) or as late as last.

In the other template, with H before R, S, and T, we don't know where T falls in that order, so we can split it into two sub-templates, one in which G is before T (forcing T to be last, because it must also be after both R and S), and one in which T is before G, in which case the order of T relative to R and S is completely undetermined and therefore entirely flexible. In that case, T could be as early as second (because it must still be after H) and as late as fourth (because it must be before G). It could also fall in the third spot, between R and S in either order.

Draw that all out and you will have three templates that cover every possible solution to the game!

[cgleeson]

Thank you so much Renatta ....this explained everything to me!

Hi PowerScore! Is it possible for someone to kindly post a diagram of the templates and rules for this game? I am struggling to wrap my head around how the diagramming should look for this question. I would really appreciate it, thank you!

For anyone else in the future looking, I found some diagrams here: lsat/viewtopic.php?t=16230

[baughy878]

Hello!

I think I struggle with recognizing when I should and shouldn't make templates. For this PT 83, I took way too long on both this LG and the last one because I missed the template setup. Can you elaborate on the maybe the steps to knowing I should make a template AND how to organize them? I know that's a complex answer, so no worries if it cannot be answered.

[Dana D]

Hey Baughy,

We want to use templates when the games present us with a very limited number of possible outcomes. Sometimes this is easy to see, sometimes it is not as readily apparent.

Some easy examples of when you might want to make a template to represent a limited outcome would be in a linear game like this one where you are told Hazel must either perform first or last. That rule tells us there are only 2 possible ways for the game to work, either with Hazel in the first slot or with Hazel in the last.

With this game, rule #2 might not initially appear to offer this type of very limited outcome, but in reality it does. The rule tells us what happens if Gloria performs earlier than Toshiro. The only other option for this linear game is for Gloria to perform later than Toshiro, because the rules tell us only one person performs at a time and each only performs ones. Once we realize there are only 2 possibilities for this game, G-T or T-G, we can make templates based off that information.

This works for grouping games as well - if this game was asking us to pick 3 of the 5 people to perform at the concert rather than to order the performances and rule #2 said "If Gloria performs, then T/R and S must all perform as well" then that tells us we should probably make a template. We only have 2 options - either Gloria performs, or she doesn't. If she does perform, we know a bunch of other players are triggered, and so it's worthwhile to make a template and see where that information takes us.

I would say one good rule of thumb for when to template besides identifying binary options like the examples I just used is to look at the most restrictive rule you are given for a game and see if it triggers additional inferences or outcomes. So again using this game, the 2nd rule is so restrictive and triggers so much, let's not just read it as a vague possibility of what will happen if Gloria is before Toshiro, lets actually map that out and see how that would look on the game board, because chances are high that at least one question is going to have G-T and trigger this rule.

Hope that helps!