Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation

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Problem A. 396. (March 2006)

A. 396. The elements of families $\mathcal{A}$ and $\mathcal{B}$ are finite sets, each having at most n elements. Suppose that for an arbitrary finite set F there exist $X\in\mathcal{A}$ and $Y\in\mathcal{B}$ such that X $\cap$ Y $\cap$ F=Ø. Prove that there exist $X\in\mathcal{A}$ and $Y\in\mathcal{B}$ such that X $\cap$ Y=Ø.

(5 pont)

Deadline expired on April 18, 2006.

Statistics:

6 students sent a solution.

5 points: Erdélyi Márton, Gyenizse Gergő, Nagy 224 Csaba, Paulin Roland.

3 points: 1 student.

2 points: 1 student.

Problems in Mathematics of KöMaL, March 2006

6 students sent a solution.
5 points:	Erdélyi Márton, Gyenizse Gergő, Nagy 224 Csaba, Paulin Roland.
3 points:	1 student.
2 points:	1 student.