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