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 !

this is generic enough what limitation r u talking abt

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

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

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