Super Grouping Drill 6-61

[mgulliksen]

I am having a really big problem figuring out the contrapositives and inferences in this grouping drill. Does anyone have a full diagram I can look at?

Thank you. Not understanding this is making me feel so dumb.

[Dave Killoran]

Hi M,

Thanks for the question! I'm going to address your post in reverse order, if you don't mind. First, don't ever let this test make you feel bad or dumb! It's just a test, and it's only a measure of a narrow range of skills. I've worked with thousands of students, and every single one of them ran into problems that they didn't understand, so you are not alone and having difficulty is completely normal

In fact, there's a silver lining here because each difficulty that you encounter tells you that there's something to work on, and as you work through each one and conquer it, you are getting better and better, and becoming mentally stronger. So, take these problems as mini-challenges. Sometimes there will hardship, but you can push through, and it will be worth it!

Ok, I'm gong to stop for a second and post this answer in right now, because I don't want you to feel bad for a single minute longer. But, I'll add a second response in just a little while that actually answers your question So, please hold on for a few, and then we'll work through this problem together until it makes sense.

Thanks!

[Dave Killoran]

Ok, here's part 2 of my answer. This time I'll talk about the drill directly.

The first thing to know about this drill is that it was intentionally made to be extremely difficult. Everyone who encounters this drill misses questions. I've never seen someone just go out and ace it (not saying it has never occurred or can't occur; it would just be rare). So, you having some difficulty with this is to be expected. It also begs the question as to why we would make a drill that's harder than pretty much any real LSAT game. Are we crazy or sadistic? No, we're neither, and there is a good reason for what we're doing. Sometimes we make drills extra hard in order to have a sort of Boot Camp effect: if we make some exercises really challenging, then the real thing won't feel so bad.

Ok, so we know the drill is really difficult, and why we've made it that way. But what is happening in the drill that actually makes it hard? One of the reasons is that there is an extremely complex interaction between the second rule and the last rule. I suspect that it was the consequences of this interaction (as opposed to a significant issue with diagrams or contrapositives) that caused the problems you had here.

On page 6-83, there's a lengthy explanation of that 2nd rule/Last rule interaction. Did you get a chance to read that discussion in the answer key? It's the kind of thing that a lot of students skip over, but it turns out to be pretty key to understanding all of this.

That second rule by itself is also troublesome because it's built on a negative sufficient condition. Most conditional rules feature positive sufficient conditions (such as A B), and those types of statements are easy to work with because they are triggered when something happens (in the diagram I just cited case, it's when A occurs). So, all you have to do is track what's going on with the variable in question, and then when it occurs, the rule is enacted. Negative sufficient conditions only come into play when the sufficient condition variable doesn't occur. For example, if your diagram is D G, this rule is triggered when D doesn't occur. so, it's easy to forget about and not realize that you don't have D, so that means you are forced to have G. And, the contrapositive ( G D ) also features a negative sufficient condition, so that's easy to forget about too!

Remember, in grouping, it's not just the variables that are selected that can make things happen, but the unselected variables can also have an impact. In this case, when B is not selected, then exactly one of H or I occur. By the way, the contrapositive of that rule is extremely tricky, and thus it's fully discussed on page 6-83.

So, just from those two rules you've got a lot going on already. There are still 6 other rules to juggle, as well as 12 total variables. It's like a supersized game scenario, and then on top of that it's got some vicious rules. It's not easy to handle!

What I want you to do, if you don't mind, is to please go through the drill one more time, using some of the information above. Even doing that, you'll probably run into some issues, so please jot those down, and then bring them back here, and I'll solve each question with you.

Please let me know if that works for you. Thanks!

[mgulliksen]

Thank you for your reply and yes that makes sense. My question is also about the HEF LCI and BHI rules. I am having issues figuring out the contrapositives of those rules. Can you offer some guidance.

Thanks again!

[Dave Killoran]

Hi M,

Sure, I'm happy to run each of those down for you and clarify. Let's look at the following two rules first, since they are basically the same in their form:

• 3rd rule: If H occurs, then E and F both occur.
  
  7th rule: If L occurs, then C and I must also occur.

With the third rule, the diagram is as follows:


E
H +
F


The contrapositive reverses and negates each side:


E
or H
F


So, if H occurs, the the necessary condition indicates that E and F occur (resulting in HEF). If either of E or F does not occur, then H does not occur. Within this rule, then, the following outcomes are possible:


H E F

H E F

H E F

H E F

H E F


Those are the resulting possibilities just from this rule only; the other rules obviously impact the possibilities.

Moving on to the 7th rule, it is identical in form to the third rule:


C
L +
I


The contrapositive reverses and negates each side:


C
or L
I

So, if L occurs, the the necessary condition indicates that C and I occur (resulting in LCI). If either of C or I does not occur, then L does not occur. Within this rule, then, the following outcomes are possible:


L C I

L C I

L C I

L C I

L C I


The second rule is considerably more complex, but there is also a lengthy explanation of this rule and its contrapositive at the start of the answer key on page 6-83. Can you take a look at that and let me know where it starts to be unclear? That will help me focus my answer on the exact spot that is troubling you.

Thanks!

[mgulliksen]

Dave,

I apologize for my delayed response. This makes sense thank you so much. I was wondering if you could layout the sequence of possibilities for this game but if it too lengthy I understand. I just want to make sure my diagram matches.

Thanks!

Meaghan

[Dave Killoran]

Hi Meaghan,

Thanks for the reply! Can you clarify what you mean about "the sequence of possibilities?" If you mean all the rule diagrams, sure, I'd be happy to do that If you mean every solution to the game, I'm not sure that would be too helpful, especially since it isn't how I'd go about attacking this particular game (too many variables!). Please let me know what you are thinking, and I'll do what I can to help.

Thanks!

[mgulliksen]

Hey Dave,

I am just looking for the Rule Diagrams not every solution.

Thanks!

[Dave Killoran]

Hi Meaghan,

Ok, that helps, thanks! The Forum doesn't have the most powerful visual tools, but I'll do my best. I'm also going to make all the rules "flat" since spacing can be troublesome to represent properly in this format:

• Rule 1. A B
  
  Rule 2. This one is in the book, and is better represented there than I could make happen here.
  
  Rule 3. H E + F
  
  Rule 4. I K
  
  Rule 5. D E
  
  Rule 6. I can't represent this visually here, but this is a JKL not block: JKL would be surrounded by a block with a slash through it.
  
  Rule 7. L C + I
  
  Rule 8. D D ___ only

Please let me know if that helps. Thanks!

[AspiringLawyer]

Good evening. Working through the Grouping Super Drill. I am having trouble understanding the full range of answers on Question 3.

• 3. If H, J, and K all occur, which of the remaining events must occur and which of the remaining events cannot occur?
  
  I was easily able to identify E, F, and I must occur. E and F because of Rule 3 (H E + F) and I because of Rule 4 (I K). Your answer key lists B under must occur, too. The explanation is "Since both H and I now occur, B must occur." Where did you get this from? Rule 2 does address all three of these variables: Not B H or I. The contrapositive would be Not H + Not I B. I did go back to the beginning of the Answer Key and notice you break up Rule 2 into two different rules. I don't understand how "but not both" creates the second rule you list. To me, "but not both" is already implied in "or."

Can you please help clear up this confusion? Many thanks in advance.