## Simple diagram question: Not All A is B

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lovejopd

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Joined: Tue Dec 01, 2009 1:00 pm

### Simple diagram question: Not All A is B

Hello, I have a simple question that confuses me a little bit...

I know
all A is B: A --> B
no A is B: A --> ~B

but,

How should I correctly diagram this?
Not all A is B

Does that imply
1) Some A is B: Some A --> B
2) All A is NOT B: A --> ~B (the same as no A is B)
3) ~(A-->B)

The question that I am dealing with is
A(work of art) --> B(intense feeling)
A(work of art)
Thus, B(intense feeling)
BUT ~B(no intense feeling), so it must be either ~A(not work of art) or Not all A is B(Not all work of art brings about intense feeling)

I am sorry if this question has been asked before and/or this question is stupid But I really appreciate your help!

SanDiegoJake

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### Re: Simple diagram question: Not All A is B

You can't diagram "Not all A is B" in the same way, with an arrow indicating any causality or drawing any conclusions.

However, you also cannot interpret that statement to mean that Some A is B. "Not all" means exactly what it says. It's not all. It may be true that NO A's are B's, and it may be true that SOME A's or B's. So actually none of your implications are correct. You certainly cannot conclude that no A's are B's.

What's the prep test and question number of the question you are dealing with - the one about art and evoking feeling? I can help explain if I can see the actual question.

20130312

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Joined: Wed Nov 09, 2011 8:53 pm

### Re: Simple diagram question: Not All A is B

Not all A is B means EITHER (Some A is B) OR (No A is B) BUT NOT (All A is B). So in formal logic:

(A some B) v (A -> ~B)
~(A -> B)

lovejopd

Posts: 544
Joined: Tue Dec 01, 2009 1:00 pm

### Re: Simple diagram question: Not All A is B

SanDiegoJake wrote:You can't diagram "Not all A is B" in the same way, with an arrow indicating any causality or drawing any conclusions.

However, you also cannot interpret that statement to mean that Some A is B. "Not all" means exactly what it says. It's not all. It may be true that NO A's are B's, and it may be true that SOME A's or B's. So actually none of your implications are correct. You certainly cannot conclude that no A's are B's.

What's the prep test and question number of the question you are dealing with - the one about art and evoking feeling? I can help explain if I can see the actual question.

Thank you so much for your explanation!
So Not all simply means "NOT 100%" It could be No (0%) or some (>0%). So maybe best diagram could be ~(A-->B)?

It is a Parallel question PT 41(Oct 2003) Sec 1 #15.

I really appreciate your further help as I was not familiar with the negation of (A-->B, A, Then B) even though I can simply negate A-->B to ~B --> ~A

lovejopd

Posts: 544
Joined: Tue Dec 01, 2009 1:00 pm

### Re: Simple diagram question: Not All A is B

InGoodFaith wrote:Not all A is B means EITHER (Some A is B) OR (No A is B) BUT NOT (All A is B). So in formal logic:

(A some B) v (A -> ~B)
~(A -> B)

Thank you for your feedback. It looks convoluted but makes sense!

Edited!

notaznguy

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### Re: Simple diagram question: Not All A is B

Not all = "some"

Not all A is B is diagrammed as:
A some B

sailormoon

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### Re: Simple diagram question: Not All A is B

"Not all A is B" <=> (All A are B)' <=> exclude (All A are B) <=> (some A are B) or (no A is B)

all these are equivalent statements
Last edited by sailormoon on Fri Jan 20, 2012 3:56 am, edited 1 time in total.

VasaVasori

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Last edited by VasaVasori on Sat May 02, 2015 10:58 pm, edited 1 time in total.

suspicious android

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### Re: Simple diagram question: Not All A is B

notaznguy wrote:Not all = "some"

Not all A is B is diagrammed as:
A some B

Huh? This is not accurate. Watch out, you don't want to take those phrases to mean the same thing, or diagram it as you did. That would mean a phrase like "Not all apples are blue" would be diagrammed so as to imply "Some apples are blue".

FantasticMrFox

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Joined: Tue May 03, 2011 3:00 pm

### Re: Simple diagram question: Not All A is B

Another opportunity to procrastinate Attic Greek!

I diagrammed more than what you asked for (I found the question online) so if you'd rather do it yourself, then, just ignore my post. It's probably wrong anyways

Is this the question?
If all works of art evoke intense feelings, and this sculpture is a work of art, then it follows that this sculpture evokes intense feelings. But this sculpture does not evoke intense feelings at all. So either this sculpture is not a work of art, or not all works of art evoke intense feelings

[Vx(Ax -> Fx) & As] -> Fs
~Fs
~[Vx(Ax -> Fx) & As]
therefore ~Vx(Ax -> Fx) v ~As

Note: Vx is the universal quantifier and later, I switch to U because Vitamin is also V and I can't seem to enter symbols here But you can just ignore the quantifier because InGoodFaith's diagram of your question looks exactly the same and mean, generally, the same thing.

(A) If all classes are canceled, and the biology lab is a class, then it follows that the biology lab is canceled. But the biology lab is not a class. So the biology lab is not canceled, or some classes are not canceled.

[Vx(Cx -> Nx) & Cb] -> Nb
~Cb
(You want the negation of the consequent)

(B) If all medical research is significant, and this research is medical, then it follows that this research is significant. But this research is actually of no significance. So not all medical research is significant, and this research is not medical.

[Vx(Mx -> Sx) & Mr] -> Sr
~Sr
(The conjunction "and" is key compared to the "or" in the question)

(C) If all vitamins are safe in large doses, and beta- carotene is a vitamin, then it follows that beta- carotene is safe in large doses. But beta-carotene is not safe in large doses. So not all vitamins are safe in large doses, or beta-carotene is not a vitamin.

[Ux(Vx -> Sx) & Vb] -> Sb
~Sb
~[Ux(Vx -> Sx) & Vb]
~Ux(Vx -> Sx) v ~Vb

That's the same as the question so C is the answer...I think Hopefully I didn't make a fool out of myself.

I found the question here: TestMaster June 2007 (LinkRemoved)

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### Re: Simple diagram question: Not All A is B

SanDiegoJake wrote:You can't diagram "Not all A is B" in the same way, with an arrow indicating any causality or drawing any conclusions.

For the purposes of the test, diagramming the statement is not globally useful. For example, such a condition does not appear in logic games. In LR however, you will run across "squibs", also called "stimuli" in which "not all A's are B's" are given premises.

The correct way to diagram it is to write "A", then double-arrow with a "small-s" above the middle od the double-arrow, and then "B" on the left end.

This symbolizes that "Some A's are NOT B's" and "Some things that are NOT B's are A's".
This leaves open the possibility that some A's ARE B's without extrapolating anything about things that are B's. The statement that not all A's are B's makes no inference about B's...only things that are NOT B's. So this diagram would be correct.

notaznguy wrote:Not all = "some"

Not all A is B is diagrammed as:
A some B

This would NOT be correct. Notaznguy is incorrect because the intended statement can include scenarios in which absolutely no A's are B's (i.e. 0-99%). You just can't have 100%! Diagramming "A some B" excludes that scenario (i.e. 1-100%).

The correct diagram would be would be "A some B", i.e. "some A's are B, as I stated above.

VasaVasori

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Last edited by VasaVasori on Sat May 02, 2015 10:58 pm, edited 1 time in total.

lovejopd

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### Re: Simple diagram question: Not All A is B

Thank you all for awesome feedback!
I believe it will not appear on Games, but it is good to know this concept in LR.
More importantly, know how to do the contraposition of this structure

Premise1: A-->B
Premise 2: A
Conclusion: B

If ~B, it can be either 1) ~(A-->B) OR 2) ~A

Verdict: Not All A is B: Some A is NOT B / NOT 100%, 0~99.9%