Super Grouping Drill 6-61

[Francis O'Rourke]

Hi AspiringL!

The inclusion of B was due to the second rule (italics and underline mine): If B does not occur, then either H or I, but not both will occur.

This rule tells us that whenever B does not occur, we must include one, and only one of H and I. They cannot both occur, if B fails to occur. This yields an interesting contrapositive that is explained on page 6-101. In brief, if both H and I occur - as they do in question number 3 - then B must occur. If B failed to occur, then we simply could not have both H and I. Since we do have both H and I, then we can infer that B did in fact occur.

Let me know if this helps you make sense of that second rule.

One very important general rule to remember on this exam is that "or" will be used inclusively, unless otherwise stated. What this means is that "or" does not by itself tell you that only one thing must happen.

For example, if I told you in real life that I will order either the cake, or the pie for dessert, then you would assume that I am going to order only one dessert at dinner. This is an example of using "or" exclusively. We commonly use "or" to indicate that the two conditions cannot both occur.

The LSAT uses "or" a bit differently. If we had a logic game where we were being asked to order items off a menu and one rule stated "either the cake or the pie must be selected," then three things could occur: you can select the cake, you can select the pie, you can select the cake and the pie. This is what an inclusive "or" means. Even if this deviates from how you normally use the word, it is how the LSAT uses the word.

Now consider the phrase "but not both." Including this phrase at the end of an either...or statement will tell you that both conditions may not occur together. This is probably how you use "or" in day-to-day life. Thus "The pie or the cake must be included" would tell us that only two things can occur: the cake is included and the pie is excluded or the pie is included and the cake is excluded. You can only infer that the two conditions cannot both occur when the statement includes a phrase such as "but not both," "and not both," "but not at the same time," "but not together," etc....

You can read more about using "or" in conditional relationships on pages 2-52 through 2-68. And let us know if you still have questions

[jessicamorehead]

I am confused between diagramming the second and fifth rule.

Second rule: "If B does not occur, then either H or I but not both." I diagrammed this as ~B (H I)

Fifth rule: "D and E cannot occur together." I diagrammed this as D E


Is there a difference between these rules? I'm really confused.

[Jamena Pirone]

Hi Jessica!

Indeed these rules are different. Let's remove the "if B does not occur" portion of Rule 2 for now to focus on the confusing part. So we have "Either H or I, but not both" versus "D and E cannot occur together". The functional difference is that under these rules, D and E could both be out, whereas H and I could NOT both be out (because we need either one or the other). Let's dig in deeper:

· Either H or I, but not both
This rule actually presents 2 conditional ideas, one of which is the concept of "either/or", and the other of which is "but not both". You therefore need 2 diagrams to fully represent this rule:

1) One diagram for "either/or"
Either/or is always diagrammed with the negated variable FIRST, so:
~H I
Even when you form the contrapositive, you'll see that the negated variable is still first:
~I H

When the negated variable is first, it means you have an either/or relationship between the 2 variables. (Using a biconditional arrow to represent this idea would look like so: ~H ~I)

Now here's where is gets really confusing. On the LSAT, unlike in layman's speech, "either/or" doesn't necessarily preclude both things from occurring. If they had said only "either H or I" it could mean 3 things: only H occurs, only I occurs, or BOTH occur. However, here they've added "but not both" so our options are now limited to 2 things: H being in with I out, or I being in with H out. So, we need to represent this new idea of "but not both".

2) Second diagram for "but not both"
But not both is always diagrammed with the negated variable LAST, so:
H ~I and its contrapositive
I ~H

When the negated variable is the last one of the pair, it means you can't have both variables occurring at the same time, or in other words, "but not both" (The biconditional arrow would look like this: H I)

So to summarize, you need 2 sets of diagrams for "Either H or I, but not both":
·~H I and its contrapositive ~I H (this represents either/or)
·H ~I and its contrapositive I ~H (this represents but not both)

(Note, you can actually encompass all 4 ideas with ~H I, but that's another complex post of its own!)


·D and E cannot occur together
Unlike the first rule which said "either/or but not both", this rule is ONLY saying "but not both".

Therefore, you diagram it with the negated variable last, like any "but not both" idea:
D ~E and its contrapositive
E ~D

(The biconditional being D E)

This expresses the notion that you can't have both variables occur, while leaving open the possibility that both variables are out. This possibility is left open because, for example, if D is out (that is, ~D), we have no information on what to do. ~D isn't one of the sufficient conditions, so E is free to do what it pleases. It can be in or out. Likewise, if E is out (~E), D is free to be in or out since ~E isn't one of the sufficient conditions.

This is indeed a very confusing concept, but I hope I have shed some light on it. Please let me know if anything remains unclear.

[jessicamorehead]

Jamena,

That was so helpful and concise! Thank you for taking the time to type that all out. I made a summary sheet of the conditionality rules and added your clarifications to it.

I now completely understand why the "either or, but not both" rule requires two separate diagrams since they are two different rules. When combined, the rule simply means one of the variables will be in, and the other out. Would I be able to simplify this rule to the following when diagramming:

~B (H/I) and then continue diagramming the rules directly on to H and I?

[jessicamorehead]

Actually, one more question. On question number 12 (pg 6-67) I found two possible ways to maximize the "in" group. The book only lists one correct way, so I want to make sure my other variable set is also valid.

The one listed in the book: 9 variables - B, H, E, F, I, K, J/L, C, G
The one I came up with: also 9 variables - A, I, K, J/L, C, E, F, G, H

Please let me know if I am making a mistake in thinking there are two possible ways to find the maximum of 9 variables!

Thanks,
Jessica

[Jamena Pirone]

Jessica,

Thank you for the follow-up question, as I forgot to re-connect the "IfB does not occur" portion of Rule 2, and explain how that plays out!

Because this is such a complex rule with the addition of "~B ", it helps to simplify the concepts into a more visual form. Once you understand the mechanics behind why "Either/or, but not both" leaves only 2 possibilities (H in and I out, or I in and H out), you are better served here by diagramming in a way that is visually impactful.

That being said, you still need two diagrams. What you wrote, ~B (H/I), represents the "either/or" concept. (You can certainly append more information to the H and the I.) To be thorough, on the side add another diagram, ~B H and I in a box with a slash through it, to visually represent the "but not both" concept, and you're all set! (Don't forget to diagram their contrapositives as well, as some important inferences come from those.)

[jessicamorehead]

Jamena,

Thank you! I took your advice and added the "but not both" rule to the side of the diagram. You are seriously so helpful, thank you!!

Jessica

[Jamena Pirone]

Actually, one more question. On question number 12 (pg 6-67) I found two possible ways to maximize the "in" group. The book only lists one correct way, so I want to make sure my other variable set is also valid.

The one listed in the book: 9 variables - B, H, E, F, I, K, J/L, C, G
The one I came up with: also 9 variables - A, I, K, J/L, C, E, F, G, H

Please let me know if I am making a mistake in thinking there are two possible ways to find the maximum of 9 variables!

Thanks,
Jessica

Hi Jessica,

Your other variable set is not correct because if those 9 variables are "in", then B is left "out." Rule 2 provides that if B is out, then either H or I but not both occur. In your list, you've got both H and I occurring!

[jessicamorehead]

Oh shoot, I completely ignored that rule since I was looking at my original diagram with ~B (H/I) and didn't consider the "but not both rule." I'm going to put that right next to the "either/or" rule so I don't forget it! Also, can you clarify one more concept for me?

I now understand that for "either or/but not both" rules you should diagram the "either/or" rule directly into the diagram and have the "but not both" rule next to it for visual representation.

However, if a rule is just a "but not both" one, can you directly draw that into the diagram?
For instance, I have H E and F. Then E ~D. Is that allowed, or should I keep all "but not both" rules to the side of my main diagram?

Additionally, I originally added K ~J based on the JKL not block, making a sequence of L I K ~J. Because I figured if L is in, I is in, K is in, which means J is out because all three of JKL cannot be in. However, I realized this addition was unwarranted because it entirely depends on IF L is even in. For example, I could be in without L being in, which would not automatically kick J out.

So basically, how do I know when I'm allowed to add a "but not both rule" to a diagram?

[Jamena Pirone]

Jessica,

You should always include as many rules as possible in your main diagram. Previously, when I advised you to diagram the "but not both" portion of the rule separately, it was only because, at least in the way most people diagram this drill, it doesn't fit in nicely with the other parts of the diagram. Diagramming "but not both" separately is not a hard and fast rule. That concept should absolutely be included in your diagram where, as in your example of H E and F. Then E ~D , it would fit beautifully.

As to the second part of your question, you're right that you should not have attached K ~J to the end of L I K; however, the reason is not because its a "but not both" rule, but rather because every part of your conditional chain must be able to stand on its own. As you correctly stated, K ~J only applies when L is in. When asked, you must be able to find a variable in your diagram and immediately know that everything to the right of it is always and forever true, and everything to the left of it is always and forever true in reverse (i.e.: negated if it originally was not, and un-negated if it originally was).

Your reasoning is sound. You got this!