Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping: Partially Defined game.

Most students attempt to set up this game as a map, with connections between each of the cities. But, a map setup makes it difficult to display the rules. Instead, this game is properly represented with a Grouping setup, as follows:

J03_Game_#3_setup_diagram 1.png

In this setup, each letter represents the corresponding city. There is a space above each letter where the connecting cities will be placed. At the moment, only a single space is placed above each city because we know that, at a minimum, each city is connected with at least one other city. But, each city can have multiple connections (except Montreal) so there can be more spaces added to each city as needed.

In using this setup you must remember that the nature of the connections creates an unusual effect: because each connection has two cities, when a connection is made then each city must reflect that connection. Literally, each connection creates the placement of two variables. For example, let us say that Montreal and Vancouver are connected. In the Montreal space, we would place a V, and in the Vancouver space we would place an M, as follows:

J03_Game_#3_setup_diagram 2.png

Thus, regardless of the city or number of connections, we can see all the relationships by examining the variables above the city.

If two cities cannot be connected, Not Laws must be placed under each city. For example, we know from the second rule that Honolulu and Toronto cannot be connected. Thus, we need to place a “T” Not Law under Honolulu, and an “H” Not Law under Toronto, as follows:

J03_Game_#3_setup_diagram 3.png

It is critical that you remember that any connection will produce the placement of two separate variables (one for each city). When you know that two cities cannot be connected, that will produce two Not Laws.

In the final analysis, although this game may initially appear to be a Mapping game, it is really a Grouping game. The game is Partially Defined because we know there are a minimum number of connections and a maximum number of connections (to be discussed in question #16), but the exact number is not fixed by the rules.

Let us take a look at the complete setup and then discuss each of the rules:

J03_Game_#3_setup_diagram 4.png

• First Rule: The first rule restricts the number of connections with Montreal. As soon as any connection is made with Montreal, we can then infer that no other city will be able to connect to Montreal. We have shown this restriction by placing a “1” in a circle above the M space. If the setup was done vertically, we could put a bar at the end of the Montreal space to indicate that only one connection can be made.
  
  Second Rule: This rule produces a “T” Not Law under Honolulu, and an “H” Not Law under Toronto.
  
  Third Rule: We have shown this rule on the diagram itself with the arrow from H to T. By internally diagramming the rule in this fashion, we can be sure we will not forget the rule during the course of the game. This rule also allows us to infer that Montreal cannot be connected to Honolulu (M would also then be connected to T, violating the first rule). Hence, an “M” Not Law is placed under Honolulu, and an “H” Not Law is placed under Montreal.
  
  Because H cannot be connected to M or T, we can infer that H must, at the least, be connected to P or V; hence, we have placed a P/V dual option above H, and of course because of this third rule we then know that P or V at the minimum must be connected to T.
  
  Fourth Rule: We have internally diagrammed this rule by placing a double-not arrow between T and V, with a sub-P to indicate that Philadelphia cannot be connected to both cities.
  
  Because this game does not yield a tremendous number of inferences, heading into the questions your focus must be on the rules and how they apply to the connections for each city.

[S_Hernandez52]

Hello I have a question with Questions 3 and 4 on the Logic Game #3. I got the answers correct, but I wanted to understand that in order to get the answer for question #3 is based on just the second rule that since L is last therefore Z can't be first? Secondly, for the 4th question how I used to get to the answer is look at the hypothetical that was proven in question 1 and the rules and use those as my reference to find the answer. This method seemed a bit time consuming, wondering if there is another way to get to the correct answer. Lastly, it seems to be the case that the rules were very important in this case and could have solved me some time if I wrote those out. Thanks hopefully I am not asking too many questions.

[Charlie Melman]

Hi S,

For Question 3, you're correct. Since L is last, then L cannot be before O. Thus, the contrapositive of the second rule triggers, meaning Z can't be first. Since we've just made an inference, it's a good idea to check the answer choices to see if the inference is one of the answers. In this case it is, in the form of answer choice (A).

What I do for open-ended questions like Question 4 is to see if I can quickly get rid of any answer choices before drawing new game boards to try others. You can do so by looking linearly down your list of rules after reading each answer choice., you can immediately eliminate answer choices (A) and (D), since they contradict rules 1 and 2, respectively. Then try the remaining answer choices.

Finally, you're correct that the rules were critical in this game. You could write out:

M T
or
M K
not both

but I think you'll find that as you practice you will be able to read the notation with less and less mental effort.

Let me know if you have any other questions!

[lathlee]

Dear staff,

in this page of *Third Rule. We have shown this rule on the diagram itself with the arrow from H to T By internally diagramming the rule in this fashion, we can be sure we willl not forget the rule during the course of the game. This rule also allows us to infer that Montreal cannot be connected to Honolulu (M would also then be connected to T, violating the first rule). Hence an M"M" Not law is placed under Honolulu, and an "H" Not Law is placed under Montreal."

Now, this is where confusion begins for me. In terms of pictorial description of this explanation, in the answer sheet diagram, placed in the upper corner of pg 6-113, how H ---> T,
p/v p/v
__ ___
as picture suggest isn't this mean what variable also occurs in H ---> T


but the rule says the two cities cannot be connected but the pictorial explanation and diagram suggests If H then T .

confusion rule #2, This rule also allows us to infer that Montreal cannot be connected to Honolulu (M would also then be connected to T, violating the first rule). I do not under stand how diagramming

how H ---> T,
p/v p/v
__ ___
as picture suggest isn't this mean what variable also occurs in H ---> T

would help us ( the question solves) not violating the first rule.


also, this conditional relationship expression drove me crzazy

what does ---h ----T means here in the diagram placed in 6-113 as the third rule.

[lathlee]

Hi. Can I plz get the answer. plz. thx

[Dave Killoran]

Hi Lathlee,

Would you mind perhaps editing the initial question above to make it a bit clearer as to exactly what you are asking? We've got a lot of questions coming in right now, and this appears to have multiple questions inside it, and so it's a struggle for us to figure out exactly what you are being asked. This is affecting our ability to provide you with timely responses

Thanks!

[lathlee]

pg 1

[lathlee]

pg 2

[lathlee]

Hi. I do not understand the staff's intentions in the pg 2 of the image i posted, the third rule. how H--> T since third rule stated in this pictorial representation -h ----> -T .

cuz in pg. 6-76 game 10: june 2003 questions 11-17.
the following conditions govern zephyr's nonstop flights:

Montreal is connected with exactly one one other city.

Hnolonlu is not connected with Toronto.

Any city that is connected with Toronto. If philadephia is conncted with Toronto, then philadephia is not connected with vancouver

[nicholaspavic]

Hi lathlee,
It's an unusual diagram for an unusual rule. Our intention, as stated, is to use it to remind us during the game that M cannot be connected to H because then it would also be connected to T.

I think this clears it up, but let us know if you had a different question in mind.