Let . Suppose we have a family of subsets of such that the intersection of any three members of the family is nonempty. Show that there exists which is common to all the elements of .

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- November 5th 2009, 05:39 PMBruno J.Set theory problem
Let . Suppose we have a family of subsets of such that the intersection of any three members of the family is nonempty. Show that there exists which is common to all the elements of .

- November 5th 2009, 06:21 PMDrexel28
- November 5th 2009, 06:50 PMBruno J.
- November 8th 2009, 02:11 PMBruno J.
Hint :

__Spoiler__: - November 9th 2009, 09:22 PMBruno J.
My solution :

__Spoiler__: