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Formula for no. of items in a sets

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Formula for no. of items in a sets

by prachich1987 » Fri Jan 21, 2011 6:39 am
True # of items = (total # in group 1) + (total # in group 2) + (total # in group 3) - (# in only groups 1/2) - (# in only groups 1/3) - (# in only groups 2/3) - 2(# in all 3 groups) + (# in no groups)


Can this formula be applied to ALL sets which contain three different item or it has some limitations?

Thanks !
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by maihuna » Fri Jan 21, 2011 9:36 am
this is generic enough what limitation r u talking abt
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by VivianKerr » Sat Jan 22, 2011 6:59 pm
Hi there,

I'm also not quite clear on what you question is. This page has a nice list of set theory formulas with a Venn diagram so you can visualize it. It should help clarify: https://gmat-maths.blocked/2008/05/ ... mulas.html
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by prachich1987 » Sat Jan 22, 2011 10:21 pm
Thanks Vivian for providing the link
According to it ,

P(AuBuC) = P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + P(AnBnC)

By True # of items, I mean actual no. of item in a set.
If there are three sets, then what is the formula for calculating actual no. of items
I found below formula from one of the posts on BTG.
But I think the below formula and the one I found on the link given by you are not same.

True # of items = (total # in group 1) + (total # in group 2) + (total # in group 3) - (# in only groups 1/2) - (# in only groups 1/3) - (# in only groups 2/3) - 2(# in all 3 groups) + (# in no groups)

Please help
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by santoshs » Mon Jan 24, 2011 3:36 am
Here are some formulas that can be useful while dealing with 3 sets

Total number of people/Number of people in at least one set:
AuBuC = A + B + C - AnB - AnC - BnC + AnBnC

Number of people in exactly one set:
A + B + C - 2*AnB - 2*AnC - 2*BnC + 3*AnBnC

Number of people in exactly two of the sets:
AnB + AnC+ BnC - 3*AnBnC

Number of people in two or three sets:
AnB + AnC + BnC - 2*AnBnC

Number of people in exactly three of the sets =
AnBnC
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