Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping: Undefined game.

The game scenario establishes that a group of parents are selected from seven volunteers. The game does not establish exactly how many volunteers are in the group, and so this game is Undefined. Games of this nature appear frequently on the LSAT, and thus the lack of definition should not trouble you.

The first four rules establish simple conditional relationships, although the third and fourth rules are tricky because they hinge on a negative sufficient condition.

PT58-Sept2009_LGE-G2_srd1.png

This rule contains a sufficient condition that is negative. Thus, when S does not volunteer, V must volunteer. Via the contrapositive, when V does not volunteer, S must volunteer. Thus, when one of S or V does not volunteer, the other must volunteer (it is also possible for both to volunteer). Consequently, because either S or V, or both, must always volunteer, we can reserve a space in the volunteer group for at least one of S or V with an S/V dual-option.

An alternate representation for this rule is:

PT58-Sept2009_LGE-G2_srd2.png

This representation captures the entire meaning of the rule, namely that both S and V cannot be absent from the group.

PT58-Sept2009_LGE-G2_srd3.png

This rule also contains a sufficient condition that is negative, and works in the same manner as the prior rule. Thus, when R does not volunteer, L must volunteer. Via the contrapositive, when L does not volunteer, R must volunteer. Thus, either R or L, or both, must always volunteer.

An alternate representation for this rule is:

PT58-Sept2009_LGE-G2_srd4.png

Consequently, because either R or L, or both, must always volunteer, we can reserve a space in the volunteer group for at least one of R or L with an R/L dual-option.

PT58-Sept2009_LGE-G2_srd5.png

The representations above are only for each individual rule, and do not address any inferences. Let’s now look at the inferences that follow from the rules.

Power Chain Inference: The rules combine in such a way that a long chain is created:

PT58-Sept2009_LGE-G2_srd6.png

This tremendously long and powerful chain is made by combining, in order, the contrapositive of the fourth rule, the first rule, the second rule, the fifth rule, and the contrapositive of the third rule. Having every rule connect in one long chain is exceedingly rare. Some students look at this inference and assume it only operates if L does not volunteer. But, the rules of conditional relationships indicate that any segment of the chain is valid. Thus, for example, if R volunteers then the remainder of the chain must occur (M volunteers, then T volunteers, etc.). A contrapositive of any portion is also valid.

Note also because this chain begins with a negative sufficient condition, a number of inferences can be made regarding the relationship of L and other variables. For example, if L is not selected then T must be selected, and via the contrapositive if T is not selected then L must be selected. Thus, at least one of either L or T must always volunteer. Other inferences can also be made in the same vein, as will be discussed in question #12.

The chain also reveals that, via the contrapositive, if either F or V volunteers, then L must volunteer:

PT58-Sept2009_LGE-G2_srd7.png

However, because this inference is a contrapositive of an inference contained in the chain, we will not write it out separately. In fact there are a number of similar inferences, but because they are all contained within the chain, we will not write them out separately. You should be comfortable enough with chain conditional reasoning and contrapositives that you should not have to write each of them out individually. Once the chain is written out, they are all present.

Adding the information above leads to the final setup for the game:

PT58-Sept2009_LGE-G2_srd8.png

[imagineer]

Hi,

I had a few questions regarding the logic games with the parent volunteers as referenced in the subject.

I literally went in circles when attempting this question and while some of the logic I used helped me answer a few of the questions, they were useless or the exact opposite logic of what I had used for the other questions. If you could help me out with the questions (7-12) with explanations and reasoning, I would really appreciate it.

Below is my reasoning/ breaking down the rules

1) R--> M
M--> T

Therefore- R-->M-->T, R-->T


2) R(not)-->L

3) S(not)-->V

4) T--> F(not) and V(not)
F or V--> T(not)


Volunteer Groupings:

Grouping 1: T,S,R,M

Grouping 2: L, F or V

Based on that reasoning, the answers I got for the questions are as follows


7. I was deciding between A and C and then luckily guessed C, but i'm not 100% sure why.

8. I eliminated all the answers the first time around, then went back and decided on C, but I have no idea why the answer is B.

9. I was able to determine the correct answer, as C, given my logic above.

10. I selected D, but that was also incorrect. I eliminated B (which is the correct answer) because I thought that if M is selected, then R and T would be selected which would prevent L from being selected... I figure that there might be a flaw in the reasoning there...

11. I was able to figure out that Leah had to volunteer based on the above grouping of (L, F or V)

12. Based on the groupings I provided, it seems that all the answers could be paired... if you could explain what the question means, I think that might help me in understanding the question and the answer.

I think this is an undefined question, which is why I skipped it and came back to it at the end, but how should I approach this type of question going forward? It is very time consuming for me and I would like to be able to answer these types of questions. Any help or guidance would e greatly appreciated. Thank you again for all your assistance.

Best Regards
Raj

[Dave Killoran]

Hi Raj,

Thanks for the question. From your explanation, it appears that you may not have realized the importance of the third and fourth rules (as numbered in the game, not below). Let's consider those rules once again, and their implications.

Your diagram for both is correct, but what do they actually mean? When the sufficient condition is negated and the necessary condition is positive (as is the case in both these rules), the absence of a variable then forces the other variable to be selected. So, in the case of the third rule, if S does not volunteer, then V must volunteer. And from the contrapositive, if V does not volunteer, then S must volunteer. Thus, at all times, either S or V must volunteer (and possibly both). The same logic applies to the fourth rule, and so at all times R or L must volunteer. Thus, your diagram starts off with two spaces always reserved:


S/V R/L


This has immediate consequences. For example, look again at #7A. Either R or L must always volunteer, but neither is present in this answer, and thus (A) can be eliminated.

The guideline is this: when you see rules like the third and fourth ones here, pay extremely close attention because they are tricky to work with, and they have a powerful implication: at least one of the two variables must always be selected.

Most of the rest of the questions play games with what must, cannot, or could be true based on linking the variables. For example, look at #8:

V volunteers, so: V T M R L

F and S are unknown, meaning they could both volunteer, and hence answer choice (B) is correct.

In #10, if M volunteers, then V volunteers, and that enacts the last rule, knocking our F and V. When V is knocked out, from the third rule S must volunteer, and hence (D) is eliminated. L and R are unknown, and thus (B) could be true and is correct.

Take a look at those other questions with the info above and see if that doesn't make them a bit easier.

Please let me know me if that helps. Thanks!

[imagineer]

Thanks for your help Dave! With your trick I am now getting all the questions right on the logic games section in the allotted time. Thanks for your help!

[Brittney]

I got number 10 and 12 wrong and am not sure if I made all the inferences I should have during this game. Here is what I got:

r-->m-->t r-->t (if no T then no R)

if no S then there is a V (if no v then there is a S)

if no R then there is a L (if no L then there is a R)

if T then no F (if F then no T)

if T then no V (if V then no T)

[Nikki Siclunov]

Hi Brittney,

Your rule representations are correct, but I'm afraid you didn't do enough to combine these rules in order to form chain relationships. Without a chain, it would be rather difficult to see all the inferences that result from the combination of these rules.

Here's the chain that I would make:

no L R M T no F

from T, you need to create another branch (which is difficult to represent here due to the limitations of the forum:

T no V S

Your chain should ideally go in one direction, and represent all the relationships you have in one place. No need to write down every single inference and its contrapositive, as long as you can read the chain properly. There are, in fact, so many inferences that diagramming each one separately would be incredibly time consuming:

F L
R F
R T
R V
R S
M F
M V
M S
T S

Again, you don't need to write this down, as long as your chain is good.

Hope this helps! Let me know

[srcline@noctrl.edu]

Hello

Can someone break this down for me because the only inference that I am getting is R T. And then combining the 2nd and 5th rule to get M F and M V.

I don't see how you can combine any other variables.

Thankyou
Sarah

[Nikki Siclunov]

Hi Sarah,

Please take a look at the response I posted to Brittney, which details all the inferences you can draw from the given rules. It also outlines the conditional chain that connects virtually all of the rules in this game. Note, in particular, the contrapositive of that chain, which produces many of the inferences listed.

If you still have questions after examining my earlier post, please let us know.

Thanks!

[angelsfan0055]

Hi, I was wondering if you could diagram the contrapositive of the last rule. Or at least answer the meaning of "nor" when it comes to contrapositive?
Is the opposite of nor "And" or "or?" That is, is the contrapositive of that rule If Felicia and Verna are selected than Terry is not.

OR is it If Felicia "or" Verna are selected than Terry is not selected.

There was also a similar nor rule tested in the 4th game and I had difficulty with it, and unfortunately this section

[Adam Tyson]

Neither...nor means not this AND not that, angelsfan0055. It might look like an "or," but it's not! Look over the official explanation at the top of this thread and you'll see both the rule and the contrapositive diagrammed. The contrapositive would be if F OR V volunteers, then T does not.