- #1

CornMuffin

- 55

- 5

## Homework Statement

Let T be a family of finite subsets of the natural numbers N = {1, 2, 3,...} such that if A and B are any members of T, then the intersection of A and B is nonempty.

(a) Must N contain a finite subset F such that the intersection of A, B and F is nonempty for any sets A and B belonging to T?

(b) What if we assume in addition that all the sets in T are the same size?

I need to show that the answer is yes or provide a counter-example.

## Homework Equations

## The Attempt at a Solution

I think I am having trouble with the wording of the problem or something... because if T={{1,2},{2,3},{1,3}} then there is no F that satisfies this. If this statement meant that there exists an F for each A, and B, then F can just be the intersection of A and B... so I am probably missing something here, there's no way this is supposed to be this easy. Can someone help me understand the problem a little better?