Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Mapping Game.

On the surface this game appears to be a drawing exercise, and most students diagram the game as follows:

pt15_j95_g2_1.png

However, much like the Highways game discussed previously, this is actually a Grouping game masquerading as a Mapping game. Especially indicative are the third and fourth rules, both of which are negative Grouping rules. Since grouping is such an important principle on the LSAT, we felt it worthwhile to examine a game that has mapping elements but is controlled by grouping principles.

Although every student inevitably draws out the detection areas, it is probably easier to understand this game when it is set up in a more Linear fashion:

pt15_j95_g2_2.png

In this setup, we convert the radar areas into a grouping relationship. For example, since U is inside of R and T, in our setup we show U with arrows heading towards R and T, meaning that any variable that is in U must also be in R and T. The game scenario indicates R and S do not overlap; our diagram puts a double-not arrow between R and S to indicate that any variable in one of R or S cannot be in the other. The same relationship holds for S and U.

Note that the grouping rules involving areas R, S, T, and U are easily displayed internally within this diagram. Also, since the detection areas are now represented linearly, it is easier to show the Not Laws that apply to each plane. The game is now diagrammed in a much more familiar format and should therefore be easier to attack.

With the setup structure in hand, let’s take a moment to examine the rules and generate the remainder of the diagram. In considering this setup, remember that the game is about where each plane is at exactly noon, and thus this is a snapshot at a given time.

The first rule establishes that planes J, K, L, and M are all in a zone, and thus all four are “in” the game, and no plane is “out.” This does not mean, however, that each zone contains a plane. It is possible for a zone to have no planes in it, or more than one plane in it.

The second rule places plane J in area S, and because area S does not overlap with R or U according to the game scenario, J Not Laws can be placed on areas R and U

pt15_j95_g2_3.png

The third rule creates a negative grouping relationship between K and J. Because we have now introduced the possibility of a vertical component in the game, this can be diagrammed with a vertical not-block. Additionally, a K Not Law now appears on area S because J is already in S:

pt15_j95_g2_4.png

The fourth rule creates another vertical not-block:

pt15_j95_g2_5.png

No Not Laws immediately follow from this rule, because neither L nor M is placed in any area yet.

The fifth rule limits plane M to exactly one of the areas, which immediately eliminates M from being in U (since U is inside R and T), leading to the final diagram for the game:

pt15_j95_g2_q7.png

Before moving to the questions, take a moment to consider how the “overlapping” aspect of the areas affects the planes. For example, J is known to be in area S. However, area S also overlaps with area T, so J could also be in area T (but does not have to be in area T). Areas R and T also overlap, so a plane in one could be in the other (unless the plane is in U, in which case it must be in R and T). This overlapping aspect lends a Could Be True element to the placement of the planes, and makes the game more challenging.

Finally, remember that many games that would generally be classified as Mapping games are actually Grouping games, and so often the best approach is to diagram the Grouping relationship as your primary diagram.

[PowerSteve]

I am watching the Virtual Module that Jon Denning did for Mapping Games (from the Chapter 6 supplemental material), and in number nine, Jon explained how one can use past work to answer the question without considering any hypotheticals. My question is: from looking at our main diagram and seeing that there weren't any not laws under T, would it be premature to immediately select the answer in which J, K, L and M were all there?

One further question: I'm not sure when all of these virtual modules were recorded, but is there any updated info that would be useful to know? For instance, Jon discusses how mapping games haven't showed up since the dinosaurs roamed the earth. Since the recording have there been any mapping games? Are there any other virtual modules that there may be updated info that I should consider?

[Dave Killoran]

Hi PowerSteve,

Thanks for the questions. Let me answer your questions in reverse order. If there had been some new Mapping games since he re-recorded that, we would update the module by re-recording it to include that information. Fortunately, Mapping is about as rare as a three-headed dog, so no new Mapping games have appeared since then

The strategy you are talking about in the first question is one that I would use if time is running out and there are just a few seconds left. However, one core principle we have is that if you can double-check your work, you want to do so. Just choosing the answer with J, K, L and M is to assume that you saw every Not Law during your setup (or, more directly, that your setup is infallible). I'm not normally comfortable making that assumption, so if you can easily check that work, we generally recommend that you do so. That's why he didn't just immediately jump to that answer. Of course, your setup will often be correct, but those times when it isn't, double-checking really pays off.

Please let me know if that helps. Thanks!

[LSAT2018]

It says in the game that 'R does not intersect S' does this mean that a plane cannot be at R and S at the same time?

Also the only inferences I was able were some not-laws.
If M is in exactly one of the areas, that means it cannot be at U.
And K is not in any detection area that J is in, then it cannot be at S.
What else am I missing here?

[T.B.Justin]

It says in the game that 'R does not intersect S' does this mean that a plane cannot be at R and S at the same time?

Also the only inferences I was able were some not-laws.
If M is in exactly one of the areas, that means it cannot be at U.
And K is not in any detection area that J is in, then it cannot be at S.
What else am I missing here?

Exactly, A plane in R could be in R, R and T, or R, U and T.

I attacked this game by drawing radar areas using geometric shapes to account for the rule representations. I used an irregular hexagon for area T (in the shape of pac man), a rectangle for area R, the upper portion of pac mans mouth (triangle) for area U, the lower portion of pac mans mouth where T intersects R (triangle)represented a plane can be in R or T without being in U, and a circle for area S on pac mans backside (opposite his mouth opening).

I also used R,U,T, and S as a base for not law and to help think local questions through. That with the visual representation worked for me.

[Brook Miscoski]

Justin,

It's good that you came up with a representation that helped you work this game. This is an incredibly unusual game on the LSAT, and the basic thing is to use a system that captures the correct concepts, whether that's different sized circles or shapes.