Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping Game: Defined-Fixed, Unbalanced: Overloaded.

Oct 96_M12_game#2_L5_explanations_game#4_setup_diagram_1.png

The selection of exactly five variables means the game is Defined-Fixed. Since there are eight variables from which to select, the game is Unbalanced: Overloaded.

The second rule bears further analysis. When N is reduced, neither R nor S is reduced, and it can be inferred from the contrapositive that when R or S is reduced, N cannot be reduced. Thus, N and R cannot be reduced together, and N and S cannot be reduced together. Consequently, we have written the rule in two separate parts to fully capture this powerful information.

Because the last rule reserves two of the five spaces, it is the most important one. Any rule that controls the numbers in a game is always important, and this rule is no exception. If two of L, M, and R are reduced, then of the remaining five areas of expenditure—G, N, S, P, and W—exactly three must be reduced. And since N and S cannot be reduced together, the choice is further limited. On the diagram this has been represented with the two blocks. This separation of the variables into two groups is the key to making several powerful inferences:

• 1. Because two of the group of L, M, and R must be reduced:
  
  When L is not reduced, M and R must be reduced.
  When M is not reduced, L and R must be reduced.
  When R is not reduced, L and M must be reduced.
  
  2. Because three of the group of G, P, W, N/S must be reduced:
  
  If G is not reduced, then P, W, and N/S must be reduced.
  If P is not reduced, then G, W, and N/S must be reduced.
  If W is not reduced, then G, P, and N/S must be reduced.
  (Later it will be discovered that W must always be reduced so this final inference will not be applicable.)
  
  
  3. If G and S are reduced, then W is reduced. Since these three variables fill the reduction allotment of G, N, S, P, and W, it follows that when G and S are reduced, N and P are not reduced:
  
  Oct 96_M12_game#2_L5_explanations_game#4_setup_diagram_2.png
  4. When N is reduced, R and S are not reduced. When R is not reduced, L and M must be reduced. When L and M are reduced, P is not reduced. Thus, when N is reduced, R, S, and P are not reduced. Since there are only eight .....variables for five slots, when R, S, and P are not reduced, it follows that all five of the remaining variables must
  be reduced. Thus, when N is reduced, G, L, M, and W must also be reduced.
  
  5. When L is not reduced, M and R must be reduced, and when R is reduced, N is not reduced. Thus, when L is not reduced, N is not reduced. By the same reasoning, when M is not reduced, N is not reduced.
  
  6. When P is reduced, L is not reduced. When L is not reduced, M and R must be reduced. Thus, when P is
  reduced, M and R must also be reduced. This inference is tested directly on question #8.

Understanding how the two groups work—both separately and together—is clearly a powerful weapon against the questions. In this instance the groups are originated by the final rule, a rule concerning numbers. Always be on the lookout for rules that address the numbers in a game!

[ellenb]

Dear Powerscore,

I seem to be confused the proper way to diagram rule number 2 in this game.
I read through the explanations and it gives me the contrapositive withouth the original.

However, was the original N--->not R and not S? Could you please show the complete diagram of this statement and how do they get to the final?

And is neither nor statement usually considered as an and statement? I just want to make sure that I will not think of it as an or statement or misdiagram it in the future.

Regards,

Ellen

[Dave Killoran]

Hi Ellen,

Because of the way that rule is worded, it is actually two rules in one.

The initial diagram is indeed:

R
N +
S

Not the prettiest diagram, but we do what we can with the diagramming limits of the forum! The idea is there, at least.

So, when N is selected (which is the same as reduced in this game), you know that both R and S are reduced. The representation you see in the explanation reduces this rule to its two component parts, namely that if N is reduced then R is not reduced, and if N is reduced, then S is not reduced. In single arrow form, these appear as:

N R

N S


However, when the sufficient condition is positive and the necessary condition is negative, this means that the two conditions cannot appear together, and thus the most powerful representation is to use the double arrow:

N R

N S

Thus, you see those two representations in the explanation. This is the simplest and most powerful representation of the meaning of the rule.

In answer to your final question, yes, you are correct, "neither...nor" means that both do not occur, which can be represented with "and."

Please let me know if that helps. Thanks!

[ellenb]

Thanks Dave for answering my question.

So, when we have an "and" statement such as
A-->B and C, we can separate it?

A-->B
A-->C

However, in the book under the "and" statement rule there is nothing written that we can do this division.

Will this apply to an or statement?

A-->B or C, can we separate it?

A-->B
A-->C

Also, can we still have separate contrapositive statements for an "or" statement just like we do for an and statement?

Thanks in advance!

Regards,

Ellen

[Dave Killoran]

Hi Ellen,

It's something that we discuss in class, when the results of the rule can be seen in context (as you might suspect, not every single point can--or should--be written in the text ). In this case, the separation only works when the "and" is in the necessary (see https://blog.powerscore.com/lsat/bid-26 ... Condition/).

With "or" in the necessary, you cannot separate it because it is implying that just one of the two is necessary.

When the terms are in the sufficient, "and" can't be separated, but "or" can be separated (see https://blog.powerscore.com/lsat/bid-26 ... Condition/).

Thanks!

[ellenb]

Dear Powerscore,

I am really confused on how to diagram the second rule in this game,

If N is reduced, neither R nor S is reduced.
Is it: N--> not R and not S
and if so can we separate them just like they did in the book?
N-->not R
N-->not S

Regards,

[BethRibet]

Hi Ellen,

You're on just the right track. Yes, with a conditional statement with two necessary conditions (R & S), phrased in this way, either of the following is accurate:

N --> ~R + ~S
or
N --> ~R
N --> ~S

Which way you represent it should be primarily about what best helps you understand the rule, though in the interests of time efficiency, the first way is a little bit faster. However, if you're more confused by and/or conditions, then you can do the second if it helps ensure that you won't misinterpret what the rule is telling you.

Good luck!
Beth

[ellenb]

Thanks Beth,

How about

N --> ~R or ~S

can we break it up in the same way?

N --> ~R
N --> ~S

Regards,

Ellen

[Steve Stein]

Hey Ellen,

That's a good question--in conditional reasoning, "or" doesn't work in quite the same way as "and."

The reason that we can break up an "and" necessary condition (like the first one you asked about) is that "and" tells us that both necessarily hold true. For example, if you are applying to law schools, you have gone to college and you have gone to high school.

college
applying to law school and
high school

We since we know both to be true, we can break up the conditional statement into two statements:

applying to law school college

applying to law school high school

If you are applying to law school, you have gone to college.
If you are applying to law school, you have gone to high school.

..."or" in the context of a necessary condition only tells us that at the very least, one or the other must occur. For example:

To go to prom, you must be either a junior or a senior:
junior
prom or
senior

We would not be justified in breaking this up into two statements, because neither one would be accurate:

prom junior

This basically says that to attend prom, you must be a junior. That's not true, as we know, since seniors are allowed to attend as well...and the same goes for prom senior, another invalid statement.

Good question! I hope that's helpful--please let me know whether this is clear--thanks!

~Steve

[Echx73]

Team PowerScore,

I wanted to bounce and idea off of you to make sure I understand a concept. The first rule of the game states: "If both G and S are reduced, W is also reduce." So, I go and write out my rule. (I use 'r' for and expenditure that is reduced and I signify the ones not being reduced with an 'e').

Gr Ge
and -------> Wr Then, for the contrapositive.... We ---------->or
Sr Se

We know the 'or' means one or the other or both will not be reduced. Since this game only has two groups, we know if the W is not reduced then both G and S will be in the group not reduced. There is just no other place for them to go since there is only two groups. (This is where I am hoping you can confirm my insight) But if there were three groups say : reduced, not reduced, pending. We would not be able to rule out both G and S being in the not reduced group because 'or' means one or the other or both. So we would just simply put a GS block on one of the spaces in the not reduced group because we know one of them at least is in the not reduced group, correct? Sorry if this is a bit crazy, but I know we are going to be facing grouping games with 3.4 or maybe even 5 groups. Let me know if you need me to clarify anything.