LSAT LR Bible 2016 - "either/or... but not both" pg 198

[Rnmakrinos]

Thanks guys! Ok, so I think I'm close... let me explain my understanding and pose a couple more questions...

There's 3 different types of questions that a double-not arrow can be used for:
(1) "Either/or" <--Diagram: negative S&N w/double-not arrow
(2) "Either/or... but not both" <--Diagram: negative and positive S&N w/double-not arrow
(3) "not sure what these are called" <--Diagram: positive S&N w/double-not arrow

For (1), "either/or"...

Eg: Either John or Jack will attend the party. <--Eg from LR Bible pg 196

Diagrammed as:
Jo Ja
Ja Jo
Therefore, Jo Ja

Which gives us the following options:
From LG Bible pg 295...
(A) Jo is not selected, Ja is selected
(B) Ja is not selected, Jo is selected
(C) Both Ja and Jo are selected
(D) CANNOT OCCUR: Neither Jo nor Ja is selected

For (2), "either/or... but not both"...

Eg: Either Cindy or Clarice will attend the party, but not both. <--From LR Bible pg 198
Eg: You are either in Los Angeles or San Francisco.* <--From LR Bible pg 197
*"But not both" can be assumed due to public domain of geography.

Diagrammed as:
S N
N S
Therefore, S N
AND
S N
N S
Therefore, S N

Which gives us the following options:
From LG Bible pg 295...
(A) S is not selected, N is selected
(B) N is not selected, S is selected
(C) Both S and N are selected
(D) CANNOT OCCUR: Neither S nor N is selected
AND
From LG Bible pg 293...
(E) S is selected, N is not selected
(F) N is selected, S is not selected
(G) Neither S nor N is selected
(H) CANNOT OCCUR: Both S and N are selected

QUESTION: Would the above A-H options merely be condensed down to only A/F and B/E? So, we would say that, in "either/or... but not both" questions, there's only 2 options - S is selected, N is not selected and N is selected, S is not selected.

For (3)...

Eg: If Gomez runs for president, then Hong will not run for president. <--From LR Bible pg 207
Eg: No Xs are Ys. <--From LR Bible pg 402

Diagrammed as:
S N
N S
Therefore, S N

Which gives us the following options:
From LG Bible pg 293...
(E) S is selected, N is not selected
(F) N is selected, S is not selected
(G) Neither S nor N is selected
(H) CANNOT OCCUR: Both S and N are selected

QUESTION: Is there a common wording type / "name" for these? I'm trying to figure out if there are any specific/common indicators, but, based on the egs here, there doesn't seem to be.

Thanks to you both again for your help!!

[Rnmakrinos]

I guess my last question is basically asking... why can't "No Xs are Ys" be considered an "either/or" question?

... and I don't totally get how the movie analogy explains that relationship either (although the movie analogy did help for understanding this).

[Francis O'Rourke]

Hi Makrinos,

If you want a phrase for your third example, I would use “not both” conditionals.

The biggest issue I see in what you wrote is in your first example. The phrase “either … or” does not indicate that we can’t have both conditions occurring. This is counter to how we use the phrase in the real world. However for the LSAT, If I told you "for dessert I will order either a cake or a pie," I may very well end up ordering both the cake and the pie. The only thing that I know to be true is that I must order at least one of those two desserts.

So why can’t the statement “No Xs are Ys” be expressed with “either… or?” Well “either … or” tells us that at least one of the two conditions must occur. It’s possible that I have Z, and Zs are neither Xs nor Ys.

I’m not sure where you are finding the movie analogy. Can you provide the book and page number you are looking at?

[taylorharris24]

Sorry to post so late... I understand the examples of what Dave and Adam showed, and how you can essentially break it up into two separate rules. My only confusion is how you then turn the two rules into contraceptives. I am currently trying to do the super grouping drill and I noticed that one of the rules that uses and, does not get converted to or when you turn it into the contrapositive. Sorry to lack details, I can post the specific example later once I get my book. Could someone help clarify?

As always, thanks!!

[Jon Denning]

Hi Taylor - thanks for posting! If I understand your question correctly, you're wondering how to take contrapositives from an "either/or...but not both" type statement, where it is, as Dave notes, "two statements combined in one."

If so, let's explore it using an example, and I'll borrow from makrinos' post earlier in this thread:

Either Cindy or Clarice will attend the party, but not both

First, let's break it into its respective diagrams based on what we know must happen (or cannot happen depending on how you want to think about it).

What must happen is two-fold. First:

1. Cindy or Clarice must attend, so if one doesn't the other will: Cindy Clarice , for instance.

That immediately produces a contrapositive: Clarice Cindy

So that's one statement and its contrapositive.

What else do we know?

2. Cindy and Clarice cannot both attend, so if one does the other won't: Cindy Clarice, for instance.

Again, an easy contrapositive: Clarice Cindy

And that's all there is to it! If one is missing we know the other is present; if one is present we know the other is missing. So making contrapositives is really simple once you can see the relationships in single-arrow terms (where I think some people struggle is in dealing with double arrows and double-not arrows...they are simply the pairs of statements above combined into one, but if those prove tricky for you just ignore them and use single arrows instead ).

I hope that helps!