Question about "NOT ALL"

ljh912005
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Question about "NOT ALL"

Postby ljh912005 » Mon Mar 18, 2013 7:39 am

When the statement says NOT ALL A are B

Do you interpret it as Some A are B

Or

Do you interpret it as Some A are not B.

I think the former is correct because isn't the negation of all some?

I am having trouble

Please help me out.

Redfactor
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Re: Question about "NOT ALL"

Postby Redfactor » Mon Mar 18, 2013 7:46 am

ljh912005 wrote:When the statement says NOT ALL A are B

Do you interpret it as Some A are B

Or

Do you interpret it as Some A are not B.

I think the former is correct because isn't the negation of all some?

I am having trouble

Please help me out.


You cannot interpret it as Some A are B. If no A is B, then that still fulfills the requirement of not all A are B.

Some A are not B is correct.

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A → B ⊨ ¬B → ¬A
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Re: Question about "NOT ALL"

Postby A → B ⊨ ¬B → ¬A » Mon Mar 18, 2013 7:58 am

Not all = some not.

Not all A are B. Some A are not B.

These statements are also true if NO A are B

edit: scooped, and A does exist here. Some A are not B is an existential claim. It is stating there exists an A that is not B.

sighsigh
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Re: Question about "NOT ALL"

Postby sighsigh » Mon Mar 18, 2013 8:02 am

Latter correct, former incorrect.

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Re: Question about "NOT ALL"

Postby A → B ⊨ ¬B → ¬A » Mon Mar 18, 2013 8:21 am

ljh912005 wrote:When the statement says NOT ALL A are B

Do you interpret it as Some A are B

Or

Do you interpret it as Some A are not B.

I think the former is correct because isn't the negation of all some?

I am having trouble

Please help me out.


And for negations of all and some:

All A are B = NOT Some A that is NOT B

Some A is B = NOT All A are NOT B

All A are NOT B = NOT Some A that is B

Some A is NOT B = NOT All A are B

LSATdecember2012man
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Re: Question about "NOT ALL"

Postby LSATdecember2012man » Mon Mar 18, 2013 6:25 pm

A → B ⊨ ¬B → ¬A wrote:
ljh912005 wrote:When the statement says NOT ALL A are B

Do you interpret it as Some A are B

Or

Do you interpret it as Some A are not B.

I think the former is correct because isn't the negation of all some?

I am having trouble

Please help me out.


And for negations of all and some:

All A are B = NOT Some A that is NOT B

Some A is B = NOT All A are NOT B

All A are NOT B = NOT Some A that is B

Some A is NOT B = NOT All A are B






Not All A is B can= no As equal B, right? on a 0 to 100 scale, it means 0 to 99 percent of A can be B?

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Re: Question about "NOT ALL"

Postby A → B ⊨ ¬B → ¬A » Mon Mar 18, 2013 7:23 pm

LSATdecember2012man wrote:
A → B ⊨ ¬B → ¬A wrote:
ljh912005 wrote:When the statement says NOT ALL A are B

Do you interpret it as Some A are B

Or

Do you interpret it as Some A are not B.

I think the former is correct because isn't the negation of all some?

I am having trouble

Please help me out.


And for negations of all and some:

All A are B = NOT Some A that is NOT B

Some A is B = NOT All A are NOT B

All A are NOT B = NOT Some A that is B

Some A is NOT B = NOT All A are B






Not All A is B can= no As equal B, right? on a 0 to 100 scale, it means 0 to 99 percent of A can be B?


I wouldn't use the equals sign, but yeah. Not All A are B will remain true if it is the case that NO A is B.

Use numbers you can count instead of percentages:

If there are 100 A's and Not All A are B, then there exists (at least) one A that is NOT B and the 99 others are undetermined without more information. The 99 other A's could be B or NOT B. It doesn't matter which those other 99 are as long as you know that there is one A that is NOT B.

0 A's are B and 100 A's are NOT B: could be true
1 A is B and 99 A's are NOT B: could be true
99 A's are B and 1 A is NOT B: could be true
100 A's are B and 0 A's are NOT B: false

LSATdecember2012man
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Re: Question about "NOT ALL"

Postby LSATdecember2012man » Fri Mar 22, 2013 6:19 pm

A → B ⊨ ¬B → ¬A wrote:
ljh912005 wrote:When the statement says NOT ALL A are B

Do you interpret it as Some A are B

Or

Do you interpret it as Some A are not B.

I think the former is correct because isn't the negation of all some?

I am having trouble

Please help me out.


And for negations of all and some:

All A are B = NOT Some A that is NOT B

Some A is B = NOT All A are NOT B

All A are NOT B = NOT Some A that is B

Some A is NOT B = NOT All A are B


question on your negations. for All A are B negation, why wouldnt it be Not All A that is Not B?
Same for All A ARE NOT B negation.

Redfactor
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Re: Question about "NOT ALL"

Postby Redfactor » Fri Mar 22, 2013 9:08 pm

question on your negations. for All A are B negation, why wouldnt it be Not All A that is Not B?
Same for All A ARE NOT B negation.[/quote]

"Not all" means "at least one" / some.

So when you write Not All A are Not B, you're basically saying, "at least one" / some A is B".

You can, however, say that No A is not B. That is the logical equivalent to NOT Some A is NOT B.


All oranges are fruit. (All A are B) = No orange is not a fruit. (No A is not B)

Not All oranges are Not fruit. (Not All A are Not B)

This simply says that there exists at least one (some) orange which is a fruit. We do not, however, have any idea how many oranges are fruits. This allows for some oranges to NOT be fruits as long as at least one is.



All A are NOT B = No A is B
All oranges are Not apples. (All A are NOT B) = No orange is an apple (No A is B)

Not all A are B
Not all oranges are apples.

Again, this simply states that at least one (some) orange is not an apple. This does not preclude other oranges from being apples, as long as one of them is not an apple.

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cahwc12
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Re: Question about "NOT ALL"

Postby cahwc12 » Mon Mar 25, 2013 11:46 am

A → B ⊨ ¬B → ¬A wrote:I wouldn't use the equals sign, but yeah. Not All A are B will remain true if it is the case that NO A is B.

Use numbers you can count instead of percentages:

If there are 100 A's and Not All A are B, then there exists (at least) one A that is NOT B and the 99 others are undetermined without more information. The 99 other A's could be B or NOT B. It doesn't matter which those other 99 are as long as you know that there is one A that is NOT B.

0 A's are B and 100 A's are NOT B: could be true
1 A is B and 99 A's are NOT B: could be true
99 A's are B and 1 A is NOT B: could be true
100 A's are B and 0 A's are NOT B: false


this is a roundabout way of just saying "0-99%"

LSAT blog has a great write-up on quantifying common formal logic terms, but I can't seem to easily find it.

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Re: Question about "NOT ALL"

Postby LSAT Blog » Tue Mar 26, 2013 10:48 am

cahwc12 wrote:
A → B ⊨ ¬B → ¬A wrote:I wouldn't use the equals sign, but yeah. Not All A are B will remain true if it is the case that NO A is B.

Use numbers you can count instead of percentages:

If there are 100 A's and Not All A are B, then there exists (at least) one A that is NOT B and the 99 others are undetermined without more information. The 99 other A's could be B or NOT B. It doesn't matter which those other 99 are as long as you know that there is one A that is NOT B.

0 A's are B and 100 A's are NOT B: could be true
1 A is B and 99 A's are NOT B: could be true
99 A's are B and 1 A is NOT B: could be true
100 A's are B and 0 A's are NOT B: false


this is a roundabout way of just saying "0-99%"

LSAT blog has a great write-up on quantifying common formal logic terms, but I can't seem to easily find it.


Glad you enjoyed the post! It's under the Logical Reasoning tab at the top of the blog.

Here's the link: http://lsatblog.blogspot.com/2011/02/ls ... -some.html

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Re: Question about "NOT ALL"

Postby A → B ⊨ ¬B → ¬A » Tue Mar 26, 2013 3:02 pm

cahwc12 wrote:
A → B ⊨ ¬B → ¬A wrote:I wouldn't use the equals sign, but yeah. Not All A are B will remain true if it is the case that NO A is B.

Use numbers you can count instead of percentages:

If there are 100 A's and Not All A are B, then there exists (at least) one A that is NOT B and the 99 others are undetermined without more information. The 99 other A's could be B or NOT B. It doesn't matter which those other 99 are as long as you know that there is one A that is NOT B.

0 A's are B and 100 A's are NOT B: could be true
1 A is B and 99 A's are NOT B: could be true
99 A's are B and 1 A is NOT B: could be true
100 A's are B and 0 A's are NOT B: false


this is a roundabout way of just saying "0-99%"



for this example, you are correct




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