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General questions relating to LSAT Logical Reasoning.
 menkenj
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#82572
Hi there,

I am working my way through the LR bible and want to experience more nested conditionals. The LR bible only goes through one example in chapter 6 -- to be fair, it's two examples of the same idea where a conditional is nested with an unless necessary condition and the entire nested conditional is translated into an Either/Or conditional. I love this translation/simplification but I can't fully understand nested conditionals until I see more examples.

Are there examples of when a nested conditional would turn into an AND conditional (vs. the either/or of the LR bible)?
What other types of nested conditionals have shown up on the LSAT? Is there a complete list some where?

I know this is a bit advanced and probably rare but I'm turning into an LSAT nerd. Please help!
 Adam Tyson
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#82666
As a fellow LSAT nerd, I appreciate that, menkenj! I'm not aware of any list of just nested conditionals for you to practice with, but if you search this forum for the word "nested" you will find a lot of threads that discuss various questions involving that concept and you could back your way into finding them by what test they came from.

Most nested conditionals that I have encountered are of the "unless" variety, and those all lead to a type of "or" analysis. "If the store is open late I will go get us some ice cream unless it's raining outside" leads to "If I do not get us some ice cream then either the store is not open late or else it is raining." That's pretty typical of nested conditionals.

But while I cannot recall one on the LSAT right now, I can imagine a nested conditional using a different structure: "If the store is open late then I will go get us some ice cream if and only if it is not raining." Now, it's translated to "If I do not get ice cream and it is not raining, the store must not be open late." Or it could be read as "If the store is open late then either it is not raining and I get ice cream or else it is raining and I do not get ice cream."

What's the difference between the "unless" version and the "if and only if" version? In the former, I might go get ice cream even if it is raining. I have the option of forging ahead, with the necessary condition (raining) occurring and the sufficient condition (not getting ice cream) not occurring. In the latter, that's not an option, because it's a "both or neither" situation, with getting ice cream and not raining being sufficient for each other.

Have fun with these! I sure do!
 menkenj
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#82722
Adam Tyson wrote: Tue Dec 22, 2020 10:44 am As a fellow LSAT nerd, I appreciate that, menkenj! I'm not aware of any list of just nested conditionals for you to practice with, but if you search this forum for the word "nested" you will find a lot of threads that discuss various questions involving that concept and you could back your way into finding them by what test they came from.

Most nested conditionals that I have encountered are of the "unless" variety, and those all lead to a type of "or" analysis. "If the store is open then late I will go get us some ice cream unless it's raining outside" leads to "If I do not get us some ice cream then either the store is not open late or else it is raining." That's pretty typical of nested conditionals.

But while I cannot recall one on the LSAT right now, I can imagine a nested conditional using a different structure: "If the store is open late then I will go get us some ice cream if and only if it is not raining." Now, it's translated to "If I do not get ice cream and it is not raining, the store must not be open late." Or it could be read as "If the store is open late then either it is not raining and I get ice cream or else it is raining and I do not get ice cream."

What's the difference between the "unless" version and the "if and only if" version? In the former, I might go get ice cream even if it is raining. I have the option of forging ahead, with the necessary condition (raining) occurring and the sufficient condition (not getting ice cream) not occurring. In the latter, that's not an option, because it's a "both or neither" situation, with getting ice cream and not raining being sufficient for each other.

Have fun with these! I sure do!

Hey Adam, thanks for the response. This is great!

"If the store is open late then I will go get us some ice cream unless it's raining outside"
  • "If the store is open late then either I will get us some ice cream or it's raining outside." <<< this translation is from the LR bible but feels awkward. (("If you want a table at this restaurant you have to wait, unless you have a reservation." >> Table :arrow: Wait or Reservation))
  • "If I do not get us some ice cream then either the store is not open late or else it is raining." <<< Your translation makes more sense intuitively but doesn't seem to line up to the LR bible logic.
Can you please connect the two translations for me?



Side note: For the traditional (if then)/ unless >> either/or nested conditional, does the either/or but not both translate contextually? In the book the example, "If you want a table at this restaurant you have to wait, unless you have a reservation," the translation to "Table :arrow: (Wait or Reservation)" seems to imply either or but not both. The implication is contextual rather than purely logical. Is that a fair assessment? Or is it always either/or but not both?

Thanks!
Julie
 menkenj
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#82723
To expand my understanding, I wrote an example to work through.

"Any law professor possesses a Yale Law School degree unless their scholarship is worthy."
  • If your scholarship is worthy, having a YLS JD is no longer a requirement for being a law professor.
  • Any professor of law is either a YLS alumn or has worthy scholarship.
  • ~(Law Professor :arrow: YLS JD) :arrow: Worthy Scholarship
  • Law Professor :arrow: YLS JD or Worthy Scholarship
Assume Law Professor then,
  • ~YLS JD :arrow: Worthy Scholarship
  • ~Worthy Scholarship :arrow: YLS JD

The "unless" condition does not logically force a "but not both" condition. For the law professors example, one can have both worthy scholarship and a JD from Yale.
The "unless" breaks the conditional such that the necessary statement of the initial conditional is lessened in its logical force. The "unless" operates as a logical override.

Perhaps this is also why we can extend your ice cream translation to law professors.
  • If someone is not a law professor then either they do not have a Yale Law degree or else they have worthy scholarship.

Or can we? Intuitively, it seems like it should translate to "If someone is not a law professor then either they do not have a Yale Law degree or else they do not have worthy scholarship."

Ahh I think switched the terms. It should be:

"If someone does not have a JD from Yale, then either they are not a law professor or they have worthy scholarship."
  • ~Yale JD :arrow: Not a Law Professor OR Worthy Scholarship
This seems like it really means "OR law professor with worthy scholarship"
So this implies that if they are a law professor and do not have a JD from yale, then they must have worthy scholarship.
  • (~Yale JD + Law Professor) :arrow: Worthy Scholarship
Thoughts?
 Adam Tyson
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#84124
For the ice cream example, both of those translations are valid, the second one being a form of the contrapositive of the first one. Another version of the contrapositive would be "if it is not raining, then either I get us some ice cream or else the store is not open late." There are others, too - these can be fairly flexible in how you choose to word them, as long as the logical relationships remain the same.

For your law professor example, you made a mistake but then corrected yourself . If someone is NOT a law professor, then we don't know anything. They might have a JD from Yale, or not, and they might have worthy scholarship or not. The failure of a Sufficient Condition proves nothing about the Necessary Condition, and that's just as true of Nested Conditionals as it is of "normal" conditionals.

Either/Or always allows both, from a logical perspective, unless the argument explicitly states otherwise or if the two terms being considered are inherently mutually exclusive (such as "then you will either have ice cream or you will not"). Regarding this from your earlier post:
In the book the example, "If you want a table at this restaurant you have to wait, unless you have a reservation," the translation to "Table :arrow: (Wait or Reservation)" seems to imply either or but not both.
This does not imply "but not both," because you could have a reservation and still have to wait. Happens all the time - "Your table isn't ready yet, ma'am, but we will have it ready shortly. Meanwhile, please take a seat at the bar and your server will come and get you when it's ready." Nothing about this conditional relationship alters that logic - you might have to wait, or you might have a reservation, or you might have a reservation AND have to wait.

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