Math Is Fun Forum

tonyz1949

Member

Registered: 2007-08-04

Posts: 20

Set Notation

Sets A, B, and C have 6 members in common. Sets A and B have a total of 17 members in common. Sets B and C have a total of 10 members in common. If each member of set B is contained in at least one of the other two sets, how many members are in set B?

pi man

Member

Registered: 2006-07-06

Posts: 251

Re: Set Notation

Break B into 4 groups:
    Those members which are only in B
    Those members which are only in A and B
    Those members which are only in A and C
    Those members which are in A, B and C.

If you can find out how many members are in each of those groups, you can add them up and get the total. 

You were told there were 0 members which are only in B and 6 members which are in A, B and C.  A and B have 17 members in common but 6 are also in C so there are 11 members which are in A and B but not C.  B and C have 10 members in common but 6 of those are also in A.  So there are 4 members in B and C but not A. 

0 + 11 + 4 + 6 = 21

tonyz1949

Member

Registered: 2007-08-04

Posts: 20

Re: Set Notation

Thank You pi man