Diagram This...

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Ocean64
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Diagram This...

Postby Ocean64 » Thu Jun 16, 2011 5:08 pm

I thought I'd start a thread for people to post any interesting LR diagrams or to ask diagramming questions for others to answer.

I'll begin by something I came across today:

If it is not the case that the park contains both laurels and oaks, then it contains firs and spruces.

Diagram:
(not)L or (not)O ===> F & S
(or neither)

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suspicious android
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Re: Diagram This...

Postby suspicious android » Thu Jun 16, 2011 5:14 pm

(l & o) or (f & s)

Seems simplest to me

BigRed1988
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Re: Diagram This...

Postby BigRed1988 » Thu Jun 16, 2011 5:15 pm

For the condition to not be met, both L and O have to be present. So if either L is not present OR O is not present, then the result is that F and S have to be present.

Likewise, if either F or S are not present, then it must be true that the first condition isn't met. Meaning that both L and O must be present.

So your first version is right.



Edited after confusion.
Last edited by BigRed1988 on Thu Jun 16, 2011 5:28 pm, edited 2 times in total.

BigRed1988
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Re: Diagram This...

Postby BigRed1988 » Thu Jun 16, 2011 5:18 pm

suspicious android wrote:(l & o) or (f & s)

Seems simplest to me



Can't say this. If it is F & S then there's no reason to say it can't be L & O.



If NOT L or NOT O ----> Both F AND S
If NOT S or NOT F ----> Both L AND O

There are no rules about if L & O ARE present, just about if they are both NOT present.
Last edited by BigRed1988 on Thu Jun 16, 2011 5:32 pm, edited 1 time in total.

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Ocean64
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Re: Diagram This...

Postby Ocean64 » Thu Jun 16, 2011 5:20 pm

suspicious android wrote:(l & o) or (f & s)

Seems simplest to me


I thought so too in the beginning, but i found out that it was a mistake lol...this is from game 2 in PT B in superprep btw

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suspicious android
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Re: Diagram This...

Postby suspicious android » Thu Jun 16, 2011 6:58 pm

BigRed1988 wrote:

Can't say this. If it is F & S then there's no reason to say it can't be L & O.



If NOT L or NOT O ----> Both F AND S
If NOT S or NOT F ----> Both L AND O

There are no rules about if L & O ARE present, just about if they are both NOT present.


That's what my post said. You have to have at least one pair, maybe both. "Or" is inclusive, bro.

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suspicious android
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Re: Diagram This...

Postby suspicious android » Thu Jun 16, 2011 7:09 pm


I thought so too in the beginning, but i found out that it was a mistake lol...this is from game 2 in PT B in superprep btw


Shoulda gone with your first instinct! It's definitely correct, but so is your version in the first post. They're logically identical, just a matter of preference; I like "or" statements better than "if not".

BigRed1988
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Re: Diagram This...

Postby BigRed1988 » Fri Jun 17, 2011 9:38 am

suspicious android wrote:
BigRed1988 wrote:

Can't say this. If it is F & S then there's no reason to say it can't be L & O.



If NOT L or NOT O ----> Both F AND S
If NOT S or NOT F ----> Both L AND O

There are no rules about if L & O ARE present, just about if they are both NOT present.


That's what my post said. You have to have at least one pair, maybe both. "Or" is inclusive, bro.



"Or" is not necessarily inclusive, someone diagraming it that way might assume that it has to be one or the other, and can't be both. That makes it even more confusing. Bro.

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suspicious android
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Re: Diagram This...

Postby suspicious android » Fri Jun 17, 2011 1:27 pm

BigRed1988 wrote:"Or" is not necessarily inclusive, someone diagraming it that way might assume that it has to be one or the other, and can't be both. That makes it even more confusing. Bro.


Only if people don't understand the implications of "or" will they make this mistake, as you did in your erroneous correction. It's worth it to learn. People also very frequently misunderstand statements when diagrammed as you recommended. They're tricky. Anyway, the two diagrams are logically identical, there is no single correct answer, just a number of incorrect ones.

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soj
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Re: Diagram This...

Postby soj » Fri Jun 17, 2011 1:30 pm

when it comes to the lsat, suspicious android is never wrong

also
Image
Last edited by soj on Fri Jun 17, 2011 1:37 pm, edited 1 time in total.

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UnamSanctam
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Re: Diagram This...

Postby UnamSanctam » Fri Jun 17, 2011 1:34 pm

suspicious android wrote:
BigRed1988 wrote:"Or" is not necessarily inclusive, someone diagraming it that way might assume that it has to be one or the other, and can't be both. That makes it even more confusing. Bro.


Only if people don't understand the implications of "or" will they make this mistake, as you did in your erroneous correction. It's worth it to learn. People also very frequently misunderstand statements when diagrammed as you recommended. They're tricky. Anyway, the two diagrams are logically identical, there is no single correct answer, just a number of incorrect ones.


TITCR

The symbol for "or" (in my case "v") has always meant inclusive. You use different symbols for OR (inclusive) and XOR (exclusive).

You can diagram any logic problem by simply using AND or XOR.

BigRed1988
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Re: Diagram This...

Postby BigRed1988 » Fri Jun 17, 2011 1:38 pm

suspicious android wrote:
BigRed1988 wrote:"Or" is not necessarily inclusive, someone diagraming it that way might assume that it has to be one or the other, and can't be both. That makes it even more confusing. Bro.


Only if people don't understand the implications of "or" will they make this mistake, as you did in your erroneous correction. It's worth it to learn. People also very frequently misunderstand statements when diagrammed as you recommended. They're tricky. Anyway, the two diagrams are logically identical, there is no single correct answer, just a number of incorrect ones.



Fine, if OP can differentiate between "or" meaning one or the other and "or" meaning "at least one of" by writing it the same way, then cool. But you have to make absolutely sure you're keeping it in that context, because if someone else just looked at the diagram they would assume "or" has to mean either one or the other. The point of the thread is to discuss how to make confusing statements into diagrams that are less confusing. If you're going to use "or" I would make a point of including "At least 1" at the beginning so when you look back you are reminded that "or" is not mutually exclusive. If you can make that a mental note instead, more power to you, but I prefer to err on the side of less ambiguity. If OP knows meaning of XOR that works, I did not until last post.

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soj
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Re: Diagram This...

Postby soj » Fri Jun 17, 2011 1:42 pm

This isn't as elegant as android's solution, but you can split up the ORs in sufficient conditions.
~L -> F & S
~O -> F & S
~F -> L & O
~S -> L & O

This way you need only keep track of whether any of the sufficient conditions is satisfied.

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UnamSanctam
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Re: Diagram This...

Postby UnamSanctam » Fri Jun 17, 2011 1:43 pm

http://en.wikipedia.org/wiki/Logic_symbols


These are the symbols I've always used. Except XOR. Didn't really ever encounter it in my UG logic classes so I've always used a / for it in logic games.

HTH

BigRed1988
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Re: Diagram This...

Postby BigRed1988 » Fri Jun 17, 2011 1:55 pm

soj wrote:when it comes to the lsat, suspicious android is never wrong

also
Image




Other notable grads:


Image


Image


And applicants:

--ImageRemoved--

imjustjoking22
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Re: Diagram This...

Postby imjustjoking22 » Fri Jun 17, 2011 4:05 pm

UnamSanctam wrote:http://en.wikipedia.org/wiki/Logic_symbols


These are the symbols I've always used. Except XOR. Didn't really ever encounter it in my UG logic classes so I've always used a / for it in logic games.

HTH


XOR isn't used much at all in basic logic, since the 'inclusive or' is assumed.

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Ocean64
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Re: Diagram This...

Postby Ocean64 » Fri Jun 17, 2011 8:03 pm

It's good that I'm learning other methods, but given a game like that one (idk if you guys have seen it) I'd rather keep it as simple as possible, that game kicked my butt.
Here's another one from it:

If yews are not in the park, then either laurels or oaks, but not both, are in the park.

Diagram: (not)Y===> L or O (not both)
Inference 1: (not)L & (not)O ===> Y

pretty straight forward, but there's a second inference that may not be so apparent at first,

Inference 2: L & O ===> Y
Contrapositive: (not)Y ===> (not)L or (not)O (but not both, i.e. one must remain in)

so this is a case where the "or" was not inclusive because of the original rule, and when looking at inference 2 you can't simply do the CP without remembering the original "but not both" restriction.

any thoughts or comments?

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soj
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Re: Diagram This...

Postby soj » Fri Jun 17, 2011 8:10 pm

Your two inferences together make up the contrapositive of the original diagram. So the contrapositive of inference 2 is simply a restatement of the original diagram.

The LSAT will sometimes use OR inclusively without giving you explicit hints like "or both." In fact, whenever there is no indication whether a particular OR is inclusive or exclusive, it's inclusive. The LSAT will NEVER use OR exclusively without giving you explicit hints like "but not both."

If the inclusive OR is not intuitive for you, TCR is to practice and make it intuitive.

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EarlCat
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Re: Diagram This...

Postby EarlCat » Fri Jun 17, 2011 8:24 pm

soj wrote:This isn't as elegant as android's solution, but you can split up the ORs in sufficient conditions.
~L -> F & S
~O -> F & S
~F -> L & O
~S -> L & O

This way you need only keep track of whether any of the sufficient conditions is satisfied.


I like this way for in/out games (I might even break up the right-side "and" statements too). Its a little more to write initially, but using simple conditionals makes going through the questions more straightforward IMHO.

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EarlCat
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Re: Diagram This...

Postby EarlCat » Fri Jun 17, 2011 8:26 pm

soj wrote:The LSAT will sometimes use OR inclusively without giving you explicit hints like "or both." In fact, whenever there is no indication whether a particular OR is inclusive or exclusive, it's inclusive. The LSAT will NEVER use OR exclusively without giving you explicit hints like "but not both."

If the inclusive OR is not intuitive for you, TCR is to practice and make it intuitive.

TITCR

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Re: Diagram This...

Postby JurisDoctorate » Sat Jun 18, 2011 11:09 am

BigRed1988 wrote:For the condition to not be met, both L and O have to be present. So if either L is not present OR O is not present, then the result is that F and S have to be present.
Likewise, if either F or S are not present, then it must be true that the first condition isn't met. Meaning that both L and O must be present.
So your first version is right.
Edited after confusion.


Can you explain how you came to this?

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Re: Diagram This...

Postby JurisDoctorate » Sat Jun 18, 2011 11:14 am

Ocean64 wrote:If it is not the case that the park contains both laurels and oaks, then it contains firs and spruces.


Depending on how many things can be in the park...

Possibilities:

LFSXXX
OFSXXX
FSXXXX
LOFSXX

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Ocean64
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Re: Diagram This...

Postby Ocean64 » Sun Jun 19, 2011 10:54 am

Diagram this...

Unless Marion takes the train instead of driving, she can get to work on time only by leaving at least 45 minutes early.

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soj
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Re: Diagram This...

Postby soj » Sun Jun 19, 2011 11:46 am

Ocean64 wrote:Diagram this...

Unless Marion takes the train instead of driving, she can get to work on time only by leaving at least 45 minutes early.

That Q is a tricky one. I don't think diagramming will help you much there.

If on time -> 45min early OR train
(inclusive OR, obviously)

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suspicious android
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Re: Diagram This...

Postby suspicious android » Sun Jun 19, 2011 12:56 pm

How about:

The fact that citizens must own property in order to vote is enough to declare either that voting is not a free activity or that the only true citizens are property owners.




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