Negating an unless statement

6lehderjets
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Negating an unless statement

Postby 6lehderjets » Thu Aug 25, 2011 2:17 pm

Having a little trouble negating answer choices for assumption questions that have "unless" in them. How would negate the statement below?

People who attempt to jump of buildings are likely to do themselves more harm than good unless they have they something soft to land on...

Kind of a dark answer choice but the question stands! Thanks.

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proxy
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Re: Negating an unless statement

Postby proxy » Thu Aug 25, 2011 2:34 pm

THIS EXPLANATION IS WRONG, SEE THE ONE BELOW

The statement is an implication. Get rid of the unless by rewriting it like this:

If people who attempt to jump off buildings are NOT likely to do themselves more harm than good, then they have something soft to land on.

The negation would be the logical opposite, which is:

If people who attempt to jump off buildings ARE LIKELY to do themselves more harm than good, then they DO NOT have something soft to land on.

I'm only 70% confident in my response. Hope this helps :oops: :oops:

edit: made a correction (added the DO NOT). I think you have to distribute the negation throughout the entire expression.

Say you have the following: p --> q
The negation would be: ~(p --> q) = ~p --> ~q

The unless makes things really confusing. Just remember that when we come across it, the expression that it modifies is the necessary condition, and the sufficient condition is the negation of the remaining expression.
Last edited by proxy on Thu Aug 25, 2011 3:12 pm, edited 2 times in total.

msuz
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Re: Negating an unless statement

Postby msuz » Thu Aug 25, 2011 2:47 pm

Here's how I understand it;

LDHG: Likely to do more harm than good
SLO: Have something soft to land on

SLO -> ~LDHG
(If you have something soft to land on, then you are NOT likely to do more harm than good)

Negated:
LDHG -> ~SLO
(If you are likely to do more harm than good, then you do NOT have something soft to land on)

Granted, I'm attempting to help because sometimes I have trouble negating unless statements as well.

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proxy
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Re: Negating an unless statement

Postby proxy » Thu Aug 25, 2011 2:53 pm

msuz wrote:Here's how I understand it;

LDHG: Likely to do more harm than good
SLO: Have something soft to land on

SLO -> ~LDHG
(If you have something soft to land on, then you are NOT likely to do more harm than good)

Negated:
LDHG -> ~SLO
(If you are likely to do more harm than good, then you do NOT have something soft to land on)

Granted, I'm attempting to help because sometimes I have trouble negating unless statements as well.


Hi Msuz. That's not the negation, that's the contrapositive. I made the same mistake lol :)

msuz
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Re: Negating an unless statement

Postby msuz » Thu Aug 25, 2011 3:04 pm

msuz wrote:msuz wrote:
Here's how I understand it;

LDHG: Likely to do more harm than good
SLO: Have something soft to land on

SLO -> ~LDHG
(If you have something soft to land on, then you are NOT likely to do more harm than good)

Negated:
LDHG -> ~SLO
(If you are likely to do more harm than good, then you do NOT have something soft to land on)

Granted, I'm attempting to help because sometimes I have trouble negating unless statements as well.


Hi Msuz. That's not the negation, that's the contrapositive. I made the same mistake lol


D'oh! You're right. Guess its time to review the LR Bible, lol. Ill leave my mistake up so other people can make fun of me.

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proxy
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Re: Negating an unless statement

Postby proxy » Thu Aug 25, 2011 3:08 pm

I'm going to attempt to clean up my answer above (Thanks for asking this by the way, this is really good practice :D )

People who attempt to jump off buildings are likely to do themselves more harm than good unless they have they something soft to land on

Ok, first thing is get rid of the unless statement. The unless statement modifies the necessary condition (q), which comes after the arrow.

Code: Select all

p:
q: they have they something soft to land on

p --> q


Then, we negate the rest of the expression to get the sufficient condition (p)

Code: Select all

p: people who attempt to jump off buildings are NOT likely to do themselves more harm than good
q: they have they something soft to land on

p --> q


So the logical equivalent of the original statement is:

If people who attempt to jump off buildings are NOT likely to do themselves more harm than good, then they have they something soft to land on

Code: Select all

~(p -->q)  =   p and ~q


So the negation of the statement is

People who attempt to jump off buildings are NOT likely to do themselves more harm than good And they have they DO NOT something soft to land on
Last edited by proxy on Thu Aug 25, 2011 3:09 pm, edited 1 time in total.

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gaud
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Re: Negating an unless statement

Postby gaud » Thu Aug 25, 2011 3:09 pm

I was always told to flip the statement, then negate the second part and leave the first part alone.

so...

I will go to school unless I am sick

turns into...

If I am not sick, I will go to school.

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Jack Smirks
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Re: Negating an unless statement

Postby Jack Smirks » Thu Aug 25, 2011 3:12 pm

6lehderjets wrote:People who attempt to jump of buildings are likely to do themselves more harm than good unless they have they something soft to land on....

Edit: Never mind I forgot how to LSAT.
Last edited by Jack Smirks on Fri Aug 26, 2011 3:51 am, edited 1 time in total.

CHIJAMES11
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Re: Negating an unless statement

Postby CHIJAMES11 » Thu Aug 25, 2011 8:31 pm

I was taught to treat "unless" as "if not" and that is why I wonder if

If people who attempt to jump off buildings are NOT likely to do themselves more harm than good, then they have something soft to land on.


or if

1. The statement after "unless" becomes the necessary condition.


is correct.

Here are my reasons:

If I were to diagram this sentence "People who attempt to jump off buildings are likely to do themselves more harm than good unless they have they something soft to land on..." I would approach it this way:

If they do not (turning that unless into "if not") have something soft to land on, people who attempt to jump off buildings are likely to do themselves more harm than good. = With nothing soft, likely to do more harm than good

To follow conditional logic I then moved my "if not" statement to the beginning of the sentence because as conditional logic has taught us (if --> then) and because it makes it easier to comprehend.

In turn, I would negate this sentence as..

If they do not have something soft to land on, people who attempt to jump off buildings are UNLIKELY to do themselves more harm than good. = With nothing soft, unlikely to do more harm than good

This (the negated version) completely destroys the original sentence because, as you can obviously see, it says the probability of doing harm is not likely even though the original argument is saying it is likely . We are really not concerned with whether or not the people have something soft to land but whether landing on something not soft may or may not do more harm than good. One might also ask why I did not negate the sentence to say "If they do have something soft to land on" and that is because the MLSAT book recommends negating the word that determines how many or how often something occurs (ex: quantity words). When it is a simple sentence such as "the dog is hot" which does not have a quantity word then one can simply negate as "the dog is not hot" but this is not the case here nor is it often the case on the LSAT.

Please feel free to dissect what I have said and raise any objections for I am no lsat tutor.

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suspicious android
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Re: Negating an unless statement

Postby suspicious android » Fri Aug 26, 2011 2:26 am

Guys, guys, guys.. jeez. This is a mess. Okay, here's the number one thing to remember:

The negation of a conditional statement is NOT another conditional statement. When negating a conditional, you're really negating the relationship expressed between the two properties from the original statement. So A-->B negated becomes ~(A-->B), which can be rephrased as "A even if not B". The key to that is saying B is not really necessary, A can occur and it doesn't matter if B occurs or not. The statement "A-->~B" isn't precisely accurate, it's expressing the polar opposite of the original idea, not the logical opposite. This is a pretty fine distinction, and honestly one that isn't always necessary to make. However, it's not hard to remember.

As far as an "unless" statement, the trick is to change "unless" to "even if", and negate both elements in the sentence. So "I'll kill you unless you give me $100" becomes "I might not kill you even if you don't give me $100". For the example from the OP you'd want to say:

"People who attempt to jump off buildings are NOT likely to do themselves more harm than good EVEN IF they DON'T have they something soft to land on..."

This is the proper negation of the original sentence, which you can see by rephrasing it. The original really just meant "people who jump off buildings will hurt themselves unless they have a cushion". The negated version essentially means "People who jump off buildings don't really need cushions, they're not in danger."

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dakure
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Re: Negating an unless statement

Postby dakure » Fri Aug 26, 2011 2:51 am

Its this:

People who attempt to jump off buildings are not necessarily likely to do themselves more harm than good even if they don't necessarily have something soft to land on.



/thread

ETA: suspicious android is super close but we want to take the logical opposites as opposed polar opposites.
Last edited by dakure on Fri Aug 26, 2011 2:58 am, edited 1 time in total.

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soj
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Re: Negating an unless statement

Postby soj » Fri Aug 26, 2011 2:57 am

didn't read lol most posts ITT, but android and dakure are right.

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Blumpbeef
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Re: Negating an unless statement

Postby Blumpbeef » Fri Aug 26, 2011 3:11 am

The sentence is complicated.

"You're going to die unless you have something soft to land on" is easier.

If you don't die, then you must have had something soft to land on.

/D => S

Contrapositive:
/S => D

If you don't have something soft to land on, you're going to die for sure.

Or,

If people who jump off buildings don't have something soft to land on, they are likely to do themselves more harm than good.

CHIJAMES11
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Re: Negating an unless statement

Postby CHIJAMES11 » Fri Aug 26, 2011 3:34 am

As far as an "unless" statement, the trick is to change "unless" to "even if", and negate both elements in the sentence.


I would still change it to "if not" due to the article below

http://lsatblog.blogspot.com/2009/11/wo ... -mean.html

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crumpetsandtea
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Re: Negating an unless statement

Postby crumpetsandtea » Fri Aug 26, 2011 3:41 am

wtf this thread is so many words. fucking tl;dr and confusing as hell. This explanation is easier to grasp, I think:

http://www.top-law-schools.com/forums/viewtopic.php?f=6&t=103815#p2411364
iamtaw wrote:here is my mindless way of doing it.

make sure the sentence is in the form A unless B. ( NOT "unless B, A.")

take either A OR B and negate it.

bring the negated part of the statement to the front of an if-then statement
eg: ~A -> B (~X= NOT X)
~B -> A

hope i did a good job of explaining this haha.
pm me if need be (~pm me -> ~need be) <- couldnt help it


In this case,

A = People who attempt to jump off buildings are likely to do themselves more harm than good
B = they have they something soft to land on

~A -> B
Not likely to do more harm than good --> they have something soft
~B -> A
Dont' have something soft --> likely to do more harm than good.

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dakure
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Re: Negating an unless statement

Postby dakure » Fri Aug 26, 2011 3:57 am

DO NOT READ THIS IF YOU ARE ALREADY SET IN YOUR WAYS. IT MIGHT FUCK YOU UP


I'm not sure why you guys are trying to make the negation diagrammable. Thats what is messing you guys up. The point of a negation is not to create a sufficient necessary relationship. A negation is used to show that the necessary condition is required i.e. to show that you can't have the sufficient condition WITHOUT the necessary condition. You do this by negating the statement and comparing it to the conclusion - if it weakens the conclusion, you've shown that by eliminating the necessary condition, the argument gets worse, indicating that the necessary is in fact required. If you negate a statement and it DOESNT weaken the argument, you've shown that the condition itself is not necessary.

Take for example the following claim: James is an excellent driver.

The statement "James knows how to turn on his car" is necessary to show that James is an excellent driver (notice here that it is not sufficient to show he is an excellent driver).

To demonstrate that the condition is in fact necessary, you can negate it: "James does not necessarily know how to turn on his car." If James doesn't necessarily know how to turn on his car, it casts doubt on the argument that James is an excellent driver.

Now, the statement "James won the Daytona 500" is sufficient for us to conclude that James is an excellent driver but is it necessary? No. James could have won a different large race and that also would have been sufficient to show he is an excellent driver.

The negation of that statement "James did not necessarily win the Daytona 500" does not weaken the argument that James is an excellent driver and as such demonstrates that this is not a necessary condition for the argument "James is an excellent driver."


There is no need to make the negation into a sufficient necessary relationship. The negation "James does not necessarily know how to turn on his car" is on its own enough to demonstrate that the statement "James knows how to turn on his car" is a necessary condition in the argument "James is an excellent driver."

Similarly, the negation of "People who attempt to jump of buildings are likely to do themselves more harm than good unless they have they something soft to land on" as "People who attempt to jump off buildings are not necessarily likely to do themselves more harm than good even if they don't necessarily have something soft to land on" is enough to apply to a larger argument to determine if the statement is necessary or not. There is no need for diagramming - when you diagram, you miss certain parts of the negation that are absolutely essential, as is the case here.

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dakure
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Re: Negating an unless statement

Postby dakure » Fri Aug 26, 2011 4:04 am

If you want to DIAGRAM an unless statement, thats completely different. Diagramming a statement and diagramming its negation serve two very different purposes. Just remember this: Unless introduces the necessary condition. You then take whats remaining, put it into the sufficient condition, and you negate it.

The car stops working unless we fill it with gas.

Unless introduces the necessary. Therefore we diagram it like this:

_____ ------> we fill it with gas.

We then take the rest of the statement, put it in the sufficient condition and negate it.

The car did not stop working ---> we filled it with gas.

If the car did not stop working, then we filled it with gas.

The contrapositive then becomes:

We did not fill it with gas -----> The car stopped working.

If we did not fill it with gas, the car stopped working.

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dakure
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Re: Negating an unless statement

Postby dakure » Fri Aug 26, 2011 4:07 am

Also, i want to point out that a NEGATION is NOT the same thing as a CONTRAPOSITIVE.

Contrapositive:
A-->B
~B-->~A

Negation:
A-->B
A-->~B

A negation shows the sufficient without the necessary. A contrapositive shows the lack of a sufficient if you lack the necessary.

CHIJAMES11
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Re: Negating an unless statement

Postby CHIJAMES11 » Fri Aug 26, 2011 4:32 am

here is my mindless way of doing it.

make sure the sentence is in the form A unless B. ( NOT "unless B, A.")


But this doesn't follow the rules of logic - check out the website I linked. The only reason I bring this up is in case you encounter answer choices that say things like "the economy will get worse and moral will fade unless we become a monarchy." When I encounter AC's that look like this it is simpler for me to initially (even before negation) to read the sentence as "If we do not become a monarchy, the economy will get worse and moral will fade." I understand the quote above is for a negation but I wanted to emphasize this point because I think it may be the reason why I have a different perspective on these types of sentences. This way of viewing things also allows me to narrow my answers down by scope and relevance more efficiently because it helps me understand what the sentence is really trying to say (maybe its just me). Also, I agree with the fella above who said there is no point in diagramming it (but its easy to get carried away on these forums ha) in which case its not like I am diagramming my N/A Q's so if I have to negate I'll just apply the appropriate changes on the AC (cross out a not for example) or do it in my head. For me though, it is much easier to do it in my head when I have a clear understanding of the logical relationship between the things discussed.

330AM and I am talking about negations instead of sleeping =/

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suspicious android
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Re: Negating an unless statement

Postby suspicious android » Fri Aug 26, 2011 11:18 am

dakure wrote:People who attempt to jump off buildings are not necessarily likely to do themselves more harm than good even if they don't necessarily have something soft to land on.

ETA: suspicious android is super close but we want to take the logical opposites as opposed polar opposites.


To be super super strictly correct you can put in that first use of the word necessarily to modify "likely." However, the second time when it is modifying "have" it is extraneous. The whole point of the negation of this sentence is to say that you don't need cushioning. So even if you don't have the cushion, you may not be likely to harm yourself. So a simplified version of the sentence should read:

People are not necessarily in danger even if they don't have cushions.
Last edited by suspicious android on Fri Aug 26, 2011 11:27 am, edited 1 time in total.

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suspicious android
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Re: Negating an unless statement

Postby suspicious android » Fri Aug 26, 2011 11:21 am

CHIJAMES11 wrote:
As far as an "unless" statement, the trick is to change "unless" to "even if", and negate both elements in the sentence.


I would still change it to "if not" due to the article below

http://lsatblog.blogspot.com/2009/11/wo ... -mean.html


That article is about how to diagram an "unless" statement, not how to understand the negation of an unless statement. It's definitely true that you can just treat "unless" as "if not" when diagramming.

CHIJAMES11
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Re: Negating an unless statement

Postby CHIJAMES11 » Fri Aug 26, 2011 2:20 pm

Yes, but just to clear things up even when the statement is diagrammed using if not it can still be negated to serve the intended purpose. I don't want someone to read this who also uses "if not" to think that the negation method can't be used on an unless statement and likewise if someone can show me otherwise I would greatly appreciate it because that means I've been doing things wrong! (:

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dakure
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Re: Negating an unless statement

Postby dakure » Fri Aug 26, 2011 2:36 pm

CHIJAMES11 wrote:Yes, but just to clear things up even when the statement is diagrammed using if not it can still be negated to serve the intended purpose. I don't want someone to read this who also uses "if not" to think that the negation method can't be used on an unless statement and likewise if someone can show me otherwise I would greatly appreciate it because that means I've been doing things wrong! (:

You are confusing the contrapositive with a negation.

When you change "unless" to "if not" you are not changing the meaning of the sentence. You are changing the words used in the sentence by negating both the sufficient and necessary condition and making the necessary condition sufficient and the sufficient condition necessary. It looks like this:

A-->B
~B-->~A

The negation of an unless statement should not look like that. It should look like:
A-->B
A-->~B

Do you see the difference? The If not formula leads you to negate the sufficient and the necessary condition and then switch their places. For a negation, that is not what we want to do. We want to keep the sufficient condition the same and ONLY negate the necessary.

You will drown unless you know how to swim is diagrammed as:

~Drown ---> Know how to swim
~A ---> B

If you change unless to "if not" the sentence reads "You will drown if you don't know how to swim" which looks like:

~Know how to swim ---> Drown
~B ---> A

Thats the contrapositive argument structure:

~A --> B
~B---> A

They have IDENTICAL meanings. To negate the sentence, you want to show the sufficient condition WITHOUT the necessary condition.

Hence the negation looks like "You will not drown even if don't you know how to swim" [assuming its acceptable to use the polar opposites (in reality, we want to use the logical opposites so it really reads "you might not drown even if you don't necessarily know how to swim")]

~A--->~B

Remember, the initial diagram looked like:

~A--->B

Thus, our negation shows the sufficient condition (~A) without the necessary condition (B).

lsatisevil
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Re: Negating an unless statement

Postby lsatisevil » Fri Aug 26, 2011 2:49 pm

proxy wrote:THIS EXPLANATION IS WRONG, SEE THE ONE BELOW

The unless makes things really confusing. Just remember that when we come across it, the expression that it INTRODUCES is the necessary condition, and the sufficient condition is the negation of the remaining expression.

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suspicious android
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Re: Negating an unless statement

Postby suspicious android » Fri Aug 26, 2011 3:04 pm

dakure wrote:The negation of an unless statement should not look like that. It should look like:
A-->B
A-->~B


To negate the sentence, you want to show the sufficient condition WITHOUT the necessary condition.


The first part of your post when you corrected the 'if not' thing is right on, and the people arguing for 'if not' being the negation of an 'unless' statement are just not understanding the point at issue.

However, you're not being completely consistent with your definition of a negated conditional. In the above quoted material you do two different things. The first is not precisely correct, although is often (usually?) a close enough approximation to get a correct answer on an LR question. The latter is perfect. To see the difference consider this conditional statement:

All the men here are Russian. (M --> R)

To negate this idea, you want simply to disagree with it in the safest way possible. To show it is false, you need only to provide an example of a single man here who is not Russian. So "Some men here are not Russian" or "M some ~R" if you go for that sort of diagramming method.

M --> ~R is inconsistent with the original statement but not quite the negation. EDIT: If you meant your first example just to be a quick and dirty polar opposite, I don't mean to correct you necessarily, but it's worthwhile to note the difference.

Bottom line: The proper negation of ANY conditional statement is never going to be another conditional statement.




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