Statement Negation Drill #6, #9

[yvonne]

1. p360

The correct answer is " Not all of the missions succeeded."
How about "All of the missions didn't succeed"?
Same works?


2. p361

Statement: Unless the stock market rebounds, the economy will not recover this year.
It is written as.. -The original, unnegated statement would read 'If the economy recovers this year, then the stock market will rebound'. -
But I think right unnegated statement could be 'if the stock market doesn't rebound, the economy will not recover this year' as well. Those two sentences are same, right?
The if I make a nagation with this sentence... 'if the stock market doesn't rebound, the economy will recover this year'
Then, it's different from the right nagation answer from the book. 'If the economy recovers this year, then the stock market will not rebound'
Specifically the position of 'If' is different, and I think it's critical.
Did I miss something?

[yvonne]

1. p360

The correct answer is " Not all of the missions succeeded."
How about "All of the missions didn't succeed"?
Same works?


2. p361

Statement: Unless the stock market rebounds, the economy will not recover this year.
It is written as..
"The original, unnegated statement would read 'If the economy recovers this year, then the stock market will rebound'."

But I think right unnegated statement could be
'if the stock market doesn't rebound, the economy will not recover this year' as well.
Those two sentences are same, right?

Then, if I make a nagation with the last sentence...
'if the stock market doesn't rebound, the economy will recover this year'
Then, it's different from the right nagation answer from the book.
'if the economy recovers this year, then the stock market will not rebound'

Specifically the position of 'If' is different, and I think it's critical.
Did I miss something?

[KelseyWoods]

Hi Yvonne!

"Not all of the missions succeeded" and "All of the missions didn't succeed" don't quite mean the same thing.

"All of the missions didn't succeed" is really the polar opposite of "All of the missions succeeded."
"All of the missions didn't succeed" = "None of the missions succeeded."
"None" is the polar opposite of "All"

"Not all of the missions succeed" leaves open the possibility that some, but not all, of the missions succeeded.
"Not all" is the logical opposite of "All"

When we're negating, we want to use logical opposites. Memorize the logical opposites of quantity terms:
The logical opposite of "All" is "Not all"
The logical opposite of "None" is "Some"

Negating conditionals can be tricky! You are correct that the way you diagrammed the "unless" statement is simply the contrapositive of the way it was diagrammed in the solution and so they are logical equivalents. You are also correct that the negation you ended up with is not a contrapositive of the negation that was in the solution. But your negation is still correct. This comes back to what we're actually doing when we negate a conditional statement. When we negate a conditional statement, we aren't technically creating another conditional statement. What we're really saying is that the sufficient condition can be true even if the necessary condition is not true. That's not the same as saying that if the sufficient condition is true than the necessary condition is not true. "Even if" does not create a conditional relationship and so the negation is not really an absolute conditional statement. So your negation doesn't have to be a direct contrapositive of ours to be correct.

Here's a link to a blog post that discusses this in a bit more depth: https://blog.powerscore.com/lsat/bid-29 ... -the-lsat/

And here's more of a discussion on "even if": https://blog.powerscore.com/lsat/how-to ... nt-matter/

Hope this helps!

Best,
Kelsey

[leslie7]

Hi Yvonne!

"Not all of the missions succeeded" and "All of the missions didn't succeed" don't quite mean the same thing.

"All of the missions didn't succeed" is really the polar opposite of "All of the missions succeeded."
"All of the missions didn't succeed" = "None of the missions succeeded."
"None" is the polar opposite of "All"

"Not all of the missions succeed" leaves open the possibility that some, but not all, of the missions succeeded.
"Not all" is the logical opposite of "All"

When we're negating, we want to use logical opposites. Memorize the logical opposites of quantity terms:
The logical opposite of "All" is "Not all"
The logical opposite of "None" is "Some"

Hi Kelsey, or anyone else that can answer this.

I think in its most technical sense I can memorize the "All, not all" terms to determine the logical opposite of a statement and just plug them in. (I have read the article you posted here so ty for that).

However, I'm still unsure of what the underlying distinction is between what a Polar Opposite is vs what a Logical Opposite is.

e.g. if it weren't for those terms and the charts provided in the book how would I know just by looking at a statement if I have created a statement's logical opposite vs it's polar opposite.

For example, in this scenario I did (All of the missions did not succeed) and in reading your reply I understand the technical differentiation you made between this vs Not All of the missions succeeded

But just from looking at it how do I know that me writing "all the missions didn't succeed" is it's polar opposite just by looking at it?

(I hope this question makes sense)

I'm trying to think ahead here and ponder the possibilities that perhaps not all of the statements will have the words such as "all" to help direct how we should negate it to create its logical opposite. So is there a theoretical way to think about this that allows us to implement the logical opposite? So that when we look at a statement it's just "intuitive/natural"? Or is this technical way the only way to understand/apply it?

[leslie7]

Hi Yvonne!

"Not all of the missions succeeded" and "All of the missions didn't succeed" don't quite mean the same thing.

"All of the missions didn't succeed" is really the polar opposite of "All of the missions succeeded."
"All of the missions didn't succeed" = "None of the missions succeeded."
"None" is the polar opposite of "All"

"Not all of the missions succeed" leaves open the possibility that some, but not all, of the missions succeeded.
"Not all" is the logical opposite of "All"

When we're negating, we want to use logical opposites. Memorize the logical opposites of quantity terms:
The logical opposite of "All" is "Not all"
The logical opposite of "None" is "Some"

Hi Kelsey, or anyone else that can answer this.

I think in its most technical sense I can memorize the "All, not all" terms to determine the logical opposite of a statement and just plug them in. (I have read the article you posted here so ty for that).

However, I'm still unsure of what the underlying distinction is between what a Polar Opposite is vs what a Logical Opposite is.

e.g. if it weren't for those terms and the charts provided in the book how would I know just by looking at a statement if I have created a statement's logical opposite vs it's polar opposite.

For example, in this scenario I did (All of the missions did not succeed) and in reading your reply I understand the technical differentiation you made between this vs Not All of the missions succeeded

But just from looking at it how do I know that me writing "all the missions didn't succeed" is it's polar opposite just by looking at it?

(I hope this question makes sense)

I'm trying to think ahead here and ponder the possibilities that perhaps not all of the statements will have the words such as "all" to help direct how we should negate it to create its logical opposite. So is there a theoretical way to think about this that allows us to implement the logical opposite? So that when we look at a statement it's just "intuitive/natural"? Or is this technical way the only way to understand/apply it?

[KelseyWoods]

Hi Leslie!

Absolutely, let's talk about the difference between polar opposites and logical opposites:

Polar opposites are what you learned way back in elementary school:

Hot and cold
Easy and difficult
Tall and short
Fast and slow

They're called polar because they're at polar ends of a spectrum--hot is at one end, and cold is at the other. But aren't there things that are neither hot nor cold? What about all those temperatures on the spectrum in between hot and cold?

With logical opposites, you're basically trying to divide everything into two groups. If hot and cold are your only groups, then there are going to be a lot of things that don't go into the hot group but don't go into the cold group either. So instead, let's have a group for our "hot" things and a group for everything that is "not hot." In the "not hot" group we can put the cold things, but also the things that are lukewarm, tepid, room temperature, etc. That way everything can be divided into one of those two groups.

Though logical opposites are less familiar to us than polar opposites, they are actually simpler. At some point you really had to memorize all of those polar opposites. You were young, so you don't necessarily remember doing this and at this point it just feels like common knowledge. But logical opposites are simpler to create:

What's the logical opposite of "hot"? "Not hot."
What's the logical opposite of "easy"? "Not easy."
What's the logical opposite of "difficult"? "Not difficult."
What's the logical opposite of "tall"? "Not tall."
What's the logical opposite of "short"? "Not short."
What's the logical opposite of "fast"? "Not fast."
What's the logical opposite of "slow"? "Not slow."
What's the logical opposite of "all"? "Not all."
What's the logical opposite of "none"? "Not none", (but that's a double negative so we say that "not none" really just means the same thing as "some" or "at least one").

See the pattern? To create a logical opposite, all you need to do is add (or remove) a "not"!

That sounds a lot like negation and that's all the negation really is--taking the logical opposite of something.

When you're trying to determine if you've made a logical opposite or a polar opposite, ask yourself this: Could there be anything that doesn't fit in either of my "groups"? If the answer is yes--you don't have a logical opposite.

So if my two "groups" are "all of the missions succeeded" and "all of the missions didn't succeed," is there any other possibility that wouldn't fit in either of these "groups"? Sure! Some of the missions could succeed and some could not. Thus, these are polar opposites and not logical opposites.

But if my two "groups" are "all of the missions succeeded" and "not all of the missions succeeded," that now accounts for every possibility. The "not all of the missions succeeded" group includes the possibility that none of the missions succeeded, but it also includes the possibility that 25%, 50%, 75%, and/or 99% of the missions succeeded.

Hope this helps!

Best,
Kelsey