Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem A. 617. (May 2014)

A. 617. Let $\displaystyle \mathcal{F}$ be a finite family of finite sets and let $\displaystyle A$ be an arbitrary finite set. We say that $\displaystyle \mathcal{F}$ shatters the set $\displaystyle A$ if for every $\displaystyle X\subseteq A$ there is a set $\displaystyle F\in \mathcal{F}$ such that $\displaystyle A\cap F=X$. Show that $\displaystyle \mathcal{F}$ shatters at least $\displaystyle |\mathcal{F}|$ sets.

(5 pont)

Deadline expired on June 10, 2014.

### Statistics:

 3 students sent a solution. 5 points: Williams Kada. 0 point: 2 students.

Problems in Mathematics of KöMaL, May 2014