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Set Theory Question!

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Set Theory Question!

by bellcurve » Mon Jun 13, 2011 5:52 am
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) + 2P(AnBnC)

Why these two formulas are different (+ P(AnBnC)in the first one vs 2P(AnBnC)in the second one)?

Isn't "at least in one set" equal to union of all (AuBuC)?

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by Frankenstein » Mon Jun 13, 2011 6:07 am
Hi,
Can you post the source of this. The second formula is definitely wrong. Both the forumlas should be same.
"at least in one set" is equal to union of all (AuBuC)
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by bellcurve » Mon Jun 13, 2011 6:29 am
I saw it some other places as well. But here is one of those.

https://grockit.com/blog/gmat/2011/01/2 ... et-theory/

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by Frankenstein » Mon Jun 13, 2011 6:35 am
Hi,
That could be a silly typo, started at one place and the same has been copied in various sites. I still believe that the formula is wrong.
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by Tani » Mon Jun 13, 2011 8:01 am
To get the Total you have to take the number in each set [P(A) + P(B) + P(C)], minus the items counted twice [- P(AnB) - P(AnC) - P(BnC)], minus twice the number of items counted three times [-2 P(ABC)] plus those not in any set.
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by bellcurve » Mon Jun 13, 2011 10:35 am
I am still not sure about the equations above. Is one of them wrong? Conceptwise, what is the difference between union of all sets (AuBuc) vs "at least one set"?
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by Ian Stewart » Mon Jun 13, 2011 11:13 pm
I just looked at that blog - the number in the union of the three sets should be identical to the number who are in 'at least one set', so there's some kind of error there.

In any case, I've always found 3-overlapping set formulas both difficult to remember and awkward to apply. I would never even consider using them on a GMAT problem, and I certainly don't think you need to know them, provided you're comfortable working your way through a Venn diagram. The GMAT really is not a test of whether you are a human spreadsheet program - that is, it's not testing whether you can memorize formulas and plug numbers into them. Most GMAT questions include some kind of conceptual 'twist' so that the question is testing your ability to actually *think* through a math problem. Because of those twists, you often won't be able to simply plug numbers into some formula you've memorized to get your answer. That's one reason I much prefer a Venn diagram approach to overlapping set problems - then you aren't relying on seeing questions which ask the precise question these formulas answer.
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by Tani » Tue Jun 14, 2011 7:10 am
It's a question of what you are comfortable with. I find the formulas much more obvious and workable than Venn diagrams. By all means work with the one that makes the most sense (and produces the most right answers) for you.
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