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. 
