Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping: Undefined game.

Because the scenario does not establish any numerical information about the number of kinds of fruit carried by the stand (other than that at least one must be carried), this game is Undefined. Thus, our diagram will consist of a single space for the group:

PT36-Dec2001_LGE-G1_srd1.png

Each of the four rules is conditional in nature, and the diagram for each is as follows:

PT36-Dec2001_LGE-G1_srd2.png

Of course, the rules allow for a number of inferences. The first and second rules can be combined:

PT36-Dec2001_LGE-G1_srd3.png

This chain reduces to:

PT36-Dec2001_LGE-G1_srd4.png

The contrapositive of this rule leads to the big inference of the game:

PT36-Dec2001_LGE-G1_srd5.png

This inference allows the third rule to be restated:

PT36-Dec2001_LGE-G1_srd6.png

In addition, we can combine the first and third rules:

PT36-Dec2001_LGE-G1_srd7.png

Note that the second rule forces at least K or T to always be carried, and thus we can place a K/T dual-option in the single space representing the group. This leads to the complete setup for this game:

PT36-Dec2001_LGE-G1_srd8.png

[fritz]

Not sure if this is the right place to post this question, but thought it was worth a shot. I have been having some major issues with this game. Mainly with speed. Is there something I might be missing that will help me solve this faster?

[Jon Denning]

That's a tough game, as it is undefined numerically (you don't know how many types of fruit the stand carries) and based solely on conditional rules. So correctly diagramming the rules and their connections/consequences is key to doing well.

I think one of the most important rules--and arguably the most misunderstood--is the second, which tells you that K and T cannot both be absent. In other words, you must always have K or T (or both). The implications continue when you consider that carrying K gets rid of P (and vice versa) as well as O (from rule 3, since O needs P).

That answers questions 2 and 3, severely narrows down question 1, and certainly helps with the remaining questions as well. In fact, that rule is so powerful the test makers even force you to consider what the game would have looked like had the rule not been given (question 6).

I know that's far from a complete deconstruction, but hopefully it helps you make some progress as you go back and review that tricky game. Good luck!

JD

[ellenb]

Dear Powerscore,

I just had a quick question, why in the explanations you did not include the "both" statement for the last rule,

W--> F or T

However, there should have also been the both statement:

W--> F and T

Regards,

Ellen

[Emily Haney-Caron]

Hi Ellen!

Great question. Here, the way that rule is diagramed indicates that if W, then either figs or tangerines must be included. That diagram doesn't indicate that they can't both be included, and you're right to point out that both can be; all it is showing us is that we have a rule that there must be at least one. Does that make sense?

Emily

[srcline@noctrl.edu]

Hello Jon,

I looked back at you explanation and was still a bit confused. Specifically rules 2 and F, how would you diagram these. Also the only inference that I got was that P K because of rule 1.

Thankyou
Sarah

[Nikki Siclunov]

Hi Sarah,

The second rule states:

NO T K
Contrapositive: NO K T

It is the absence of either variable (T or K) that triggers the sufficient condition, requiring the other one to be present. In other words, at least one of T or K must always be present. This is precisely why F cannot be there by itself (the decoy answer to the second question of that game).

For more information on this particular type of conditional rule ("negative sufficient condition"), check out this Blog post:

The Most Dangerous Conditional Rule on the LSAT

Note that all the rules in this game can be combined into a chain, as follows:

O P NO K T

and also:

O W F or T

This is all you need to answer the questions

Hope this helps a bit!

[jling]

In lesson 6 game 3 (A fruit stand), the second condition is "if the stand does not carry tangerines then it carries kiwis"
I diagram it as K Not T
however Adam used Not K Not T
Can you tell me if my diagram is correct/incorrect?

ALso the last condition says "if the stand carries watermelons, then it carries figs or tangerines or both." Adam said that everytime you have an "OR rule", BOTH is already implied. Please explain why? (so even if the rule is "or" but doesn't say "both", it should be treated as "BOTH"?)

And, in question 2, "Which one of the following could be the only kind of fruit the stand carries?"
Why can't figs be the only kind of fruit? According to the diagram, O P not K T
+w T or F

F can be by itself and it does not require anything to it (versus O requires P and W, which requires not K and T

Please tell me why answer choice A) Figs is not the right choice?


Thank you,
joy

[Nikki Siclunov]

Hello Joy,

Thanks for your question, and welcome to the Forum!

Adam is correct. The rule "If no K, then T" essentially means this:

• K T
  T K

If either event does not occur, the other one has to occur. The rule does not prohibit from K and T from occurring simultaneously. Another way of wording this rule is to say:

• At least one of K or T must occur.
  Either K or T must occur.

In logic, the "either...or" construction does not preclude both events from occurring simultaneously. What cannot happen is for neither of them to occur; at least one of them must.

What Adam diagrammed is technically correct - he used the Double-Not arrow to link the two conditions (and also represent their contrapositives). Personally, I feel like this isn't a terribly helpful way to represent the rule, as it's needlessly cumbersome.

This rule is discussed at length here:

The Most Dangerous Conditional Rule on the LSAT

And here:

lsat/viewtopic.php?f=259&t=49
lsat/viewtopic.php?f=259&t=4850

The reason why F cannot be on sale by itself is precisely because either K or T must be always on sale.

Let me know if this helps.

Thanks,

[jling]

Great, and thanks, Nikki, for responding with clarity. What about the last rule when it says "if the stand carries watermelons, then it carries figs or tangerines or both." If it didn't say "or both", but instead "carries figs or tangerines", would the diagram or the logic be different?