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# Set Theory!

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Manager
Joined: 19 Nov 2010
Posts: 88

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07 Jun 2011, 07:48
I have a clearifying question about set theory formulas, if you all don't mind.

1. For 3 sets A, B, and C: P(AuBuC) = P(A) + P(B) + P(C) – P(AnB) – P(AnC) – P(BnC) + P(AnBnC)

2. No of persons in atleast one set = P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + 2 P(AnBnC)

Why these two formulas are different? Isn't "at least in one set" equal to union of all (AuBuC)?

Thanks,
BC

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Math Forum Moderator
Joined: 20 Dec 2010
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07 Jun 2011, 08:06
bellcurve wrote:
I have a clearifying question about set theory formulas, if you all don't mind.

1. For 3 sets A, B, and C: P(AuBuC) = P(A) + P(B) + P(C) – P(AnB) – P(AnC) – P(BnC) + P(AnBnC)

2. No of persons in atleast one set = P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + 2 P(AnBnC)

Why these two formulas are different? Isn't "at least in one set" equal to union of all (AuBuC)?

Thanks,
BC

I think first one is good for at least one person as well.

No idea where can we use the second formula.
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Manager
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07 Jun 2011, 09:29
Does anybody think differently?

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Current Student
Joined: 26 May 2005
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07 Jun 2011, 09:47
P(A u B u C)= P(A) + P(B) + P(C) – P(A n B) – P(A n C) – P(B n C) + 2 P(A n B n C) - atleast one

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Manager
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07 Jun 2011, 11:32

If I solve your equation using the equations above, I would get

P(A u B u C)= P(A n B n C)

Which is definatley not true. What am I missing here?

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07 Jun 2011, 11:46
bellcurve wrote:

If I solve your equation using the equations above, I would get

P(A u B u C)= P(A n B n C)

Which is definatley not true. What am I missing here?

use this
http://grockit.com/blog/gmat/2011/01/28 ... et-theory/

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Manager
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07 Jun 2011, 12:38
The link says the same thing. I have the formulas, its just that I am not sure why formula for P(AuBuC) is different than "at least one." Aren't those refering to the same things? It seems like, "at least one" is obtained by adding P(AnBnC) to P(AuBuC). What can be included in the "at least one" that can not be included in P(AuBuC)?

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Manager
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10 Jun 2011, 09:01
Can anybody shed some light?

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Veritas Prep GMAT Instructor
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13 Jun 2011, 19:55
bellcurve wrote:
Anybody?

I think that 'at least one' should be the same as union. But they seem to have something else in mind (I don't have the faintest clue what that is). In terms of the diagram, the area that corresponds to 'at least one set' according to them, doesn't represent anything.
You may want to ask them for clarification on their blog post.
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Re: Set Theory!   [#permalink] 13 Jun 2011, 19:55
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