Setup and Rule Diagrams

[Brook Miscoski]

JudicialCondor,

Your question might need to be rephrased for clarity, but I believe I understand what you are asking. In my own words, you are confused about which of the following groupings to use:

[I H] OR RRR

or, alternatively,

I [H or RRR]

or, alternatively

I H and I RRR, which is the best way to write the correct interpretation for purposes of clearing your confusion.

This can be frustrating, since the game is played in completely different ways depending on your interpretation, and most of us don't have time to see whether our assumptions are working out in the answer choices.

My advice is this:

1. if "or" led to the first interpretation above, there would have been a comma.
2. On the LSAT, "or" always means "one or the other or both" unless explicitly stated otherwise. Thus, given "Industrial can't go in a zone in which there is Housing OR three Retails" we must interpret it to mean that either of Housing or three Retails would exclude Industrial. The easiest way right now to clear up the confusion is to realize that it means that I H and I RRR.

[JudicialCondor]

Hello Brook, thanks for the reply!

Sure let me try to clarify. I’m still not seeing anything in the grammar that indicates these are definitely two rules. The lack of parallel structure in the sentence combined with the “or” really throws me. And I think I see why now.

So I read the rule as one long rule with the “or” as serving the same sufficient-negation function as the word “unless.” So I diagrammed it as [H I] —-> RRR. Does that make sense? The reason I felt this way was because there is no “in which” before “three sub zones are designated for retail use.” That lack of parallel structure in the sentence led me to read the “or” as “or else” or “unless” since the verb “are” —not clearly also covered by the preposition “in which” as the first half of the rule certainly is— actually seemed to me to be introducing a new condition guaranteed by the absence of the first: that in the absence of the previously stated proposition (that H and I are not together; so /[H I], the negation of which would be [H I]) three subzones are designated for retail use (they must be because of the nature of either or).

You see? I read the or as indicating what must be in the absence of the other condition, which I took to be that H and I cannot be together. If it’s not the case that H and I aren’t together then there must be 3 Rs. I definitely see that I’m wrong and that it makes sense as two rules if you distribute the “in which” mentally across the two clauses. But geez that felt really ambiguous. Like I thought I had done a good job dealing with another bit of test maker language trickery.

[Adam Tyson]

I think the issue, JudicialCondor (love the name!), is that you are reading an implied "or else" (which could also be seen as an implied "unless") instead of an implied "in which", and you aren't sure how to determine which interpretation is correct. The simple answer is that "unless" and "or else" cannot be taken as implied on this test, because they change meaning in ways that have to be explicit rather than implicit. The rules simply cannot, and will not be, that flexible and vague.

Imagine a parallel case in statutory law: what if we were faced with a law that stated "A licensed driver under the age of 18 may not drive a vehicle with any passengers under the age of 15 or more than one passenger between the ages of 17 and 19." Would you interpret that to mean that it would be okay for a 17-year-old driver to ride with a 14-year-old passenger as long as he had two 17-year-olds with him, too? Or would you interpret it as meaning no passengers under 15 and a maximum of one older teen? The latter makes more sense, obviously, and to interpret it the other way would strain credulity!

Here's one that's more practical for laymen: If you do not finish your vegetables you cannot have pie or cake. Am I saying you can leave veggies on your plate and have pie and cake, but not pie by itself? No way! For that to be the rule, I would have to clearly say "if you don't finish your veggies you cannot have any pie unless you also have cake" (which is crazy, but I would love that rule). It definitely means you cannot have either one if you don't finish your veggies.

The correct way to look at a structure of "not this or that" is to read it as a "neither...nor" statement, which means not this AND not that.

I hope that clears things up a bit!

[rjulien91]

Can you translate this into simpler terms? What is this saying? Within these zones, subzones can be designated for housing, industrial, or retail use, with no subzone designated for more than one use. By city regulation, a total of no more than three subzones can be designated for each of the three uses.

Setup and Rule Diagram Explanation

This is a Grouping: Undefined, Numerical Distribution game.

The game scenario establishes that within three development zones (Z1, Z2, and Z3), a maximum of three subzones can be designated for each of three uses (H, I, R):

oct12_game_4_diagram_1.png

This is a somewhat unusual Grouping game, and is clearly the most difficult game on the test. Its difficulty is due to several factors:

• 1. Min/max number of subzones overall. Although subzones can be designated for each use, neither the scenario nor the subsequent rules specify exactly how many subzones must be designated for each use. The word “can” in the second sentence of the scenario is crucial, leaving open the possibility that no subzones are being designated for any use. The rules do nothing to dispel that notion, as each rule represents a prohibition about what cannot be true, rather than an affirmation of what must be true. All we know is that the maximum possible number of subzones designated for each use is 3. The total number of subzones can be anywhere from 0 to 9.
  
  2. Min/max number of subzones per zone. Some students misread the scenario to imply that no more than three subzones of each type were possible within each zone. This is incorrect. The scenario states that no more than three subzones can be designated for each use (H, I, R), not for each zone (Z1, Z2, Z3). In fact, the minimum number of subzones per zone is 0. As a result, there are a lot of possible Numerical Distributions of subzones, as the rules are not restrictive enough to establish a minimum number of subzones per zone. If something seems too laborious, it probably is: a detailed analysis of each distribution is neither required nor encouraged.

With a group being selected, and order not important, this is a Grouping game. Because we are not required to have subzones in any of the zones, the game is Undefined. Let’s examine the rules:

The first rule establishes an R Not Law for Z1:

oct12_game_4_diagram_2.png

The second rule prohibits placing more than two H subzones in any given zone:

• max. 2H/zone

In other words, given the overall maximum of three H subzones, the second rule prohibits placing all three of them within the same zone:
oct12_game_4_diagram_3.png

The third rule establishes that a maximum of one R subzone is allowed in any zone containing an H subzone. This rule is conditional in nature, and can be represented as follows:

• H max. 1R

By the contrapositive, we can infer that any zone containing two or more R subzones cannot have any subzone designated for H:

• H ≥ 2 R

The fourth rule is actually two rules -in -one, and establishes that an I subzone is not allowed in any zone that contains either a subzone designated for H, or 3R subzones. For the sake of clarity, write these relationships out separately:

• I H
  
  I 3R

The second relationship can also be represented as a positive rule:

• I max. 2R

With all the rules properly diagrammed, let’s see if any of them can be combined to provide additional insight into the assignment of subzones to zones. While we cannot make inferences regarding the type of subzones that must (or cannot) be placed within each zone, you should notice that H appears in almost all of the rules, and as such deserves a closer look:

• Since no zone contains more than 2H’s, no zone contains both an H and an I, and no zone with an H contains more than 1R, we can infer that if any zone contains H, that zone can contain a maximum of 3 subzones (H, H, R):

• H max. 3 (H, H, R)

It may also be useful to examine the maximum number of subzones allowed if either of the other two types of subzones (R and I) were designated within any given zone:

• If a zone (other than Z1) contains an R subzone, then it can contain at most two R’s in order to allow as many I subzones as possible to be designated within it. Clearly, that zone will contain no H subzones, because those would limit the total number of subzones to 3 (see discussion above). Thus, if any zone contains R, that zone can contain a maximum of 5 subzones:

• R max. 5 (R, R, I, I, I)

• The same holds true if a zone contains an I subzone. Since I and H cannot be designated within the same zone, the maximum number of subzones allowed in that zone would be five (and not six, due to the last rule in the game):

• I max. 5 (R, R, I, I, I)

Combining all the prior information leads to the final diagram for the game:

oct12_game_4_diagram_4.png

[Adam Tyson]

Happy to help, because this game causes a lot of confusion!

First, subzones "can" be designated. That means it's an option, not a requirement. So maybe some zones are designated, but maybe not.

The next part - for housing, industrial, or retail use, with no subzone designated for more than one use - means that any subzone is for just one thing. If it's Housing, then it's just Housing. You cannot have a housing/retail combination subzone, for example.

No more than three for each use means that you cannot have more than three Housing subzones, and you cannot have more than three Industrial subzones, and you cannot have more than three Retail subzones. That's total, across all the zones. In other words, the variable set you can choose from is:

HHHIIIRRR

9 total variables, which may or may not be used (because remember, you "can" designate them, but they never said you must do so.) We have three groups in which we can place some or all of these 9 variables, and we might not place any of them.

[rjulien91]

SOOOO HELPFUL!

Happy to help, because this game causes a lot of confusion!

First, subzones "can" be designated. That means it's an option, not a requirement. So maybe some zones are designated, but maybe not.

The next part - for housing, industrial, or retail use, with no subzone designated for more than one use - means that any subzone is for just one thing. If it's Housing, then it's just Housing. You cannot have a housing/retail combination subzone, for example.

No more than three for each use means that you cannot have more than three Housing subzones, and you cannot have more than three Industrial subzones, and you cannot have more than three Retail subzones. That's total, across all the zones. In other words, the variable set you can choose from is:

HHHIIIRRR

9 total variables, which may or may not be used (because remember, you "can" designate them, but they never said you must do so.) We have three groups in which we can place some or all of these 9 variables, and we might not place any of them.