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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 points)

Deadline expired on 10 June 2014.

Statistics on problem A. 617.
 3 students sent a solution. 5 points: Williams Kada. 0 point: 2 students.

• Problems in Mathematics of KöMaL, May 2014

•  Támogatóink: Morgan Stanley