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)?
Thanks,
BC
Set Theory Question!
This topic has expert replies
-
- Legendary Member
- Posts: 1448
- Joined: Tue May 17, 2011 9:55 am
- Location: India
- Thanked: 375 times
- Followed by:53 members
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)
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)
Cheers!
Things are not what they appear to be... nor are they otherwise
Things are not what they appear to be... nor are they otherwise
-
- Senior | Next Rank: 100 Posts
- Posts: 37
- Joined: Fri Jun 25, 2010 11:07 am
- Thanked: 1 times
I saw it some other places as well. But here is one of those.
https://grockit.com/blog/gmat/2011/01/2 ... et-theory/
Thanks,
BC
https://grockit.com/blog/gmat/2011/01/2 ... et-theory/
Thanks,
BC
-
- Legendary Member
- Posts: 1448
- Joined: Tue May 17, 2011 9:55 am
- Location: India
- Thanked: 375 times
- Followed by:53 members
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.
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.
Cheers!
Things are not what they appear to be... nor are they otherwise
Things are not what they appear to be... nor are they otherwise
- Tani
- Legendary Member
- Posts: 1255
- Joined: Fri Nov 07, 2008 2:08 pm
- Location: St. Louis
- Thanked: 312 times
- Followed by:90 members
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.
Tani Wolff
GMAT/MBA Expert
- Ian Stewart
- GMAT Instructor
- Posts: 2621
- Joined: Mon Jun 02, 2008 3:17 am
- Location: Montreal
- Thanked: 1090 times
- Followed by:355 members
- GMAT Score:780
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.
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.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com
- Tani
- Legendary Member
- Posts: 1255
- Joined: Fri Nov 07, 2008 2:08 pm
- Location: St. Louis
- Thanked: 312 times
- Followed by:90 members
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.
Tani Wolff