Problem

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Tags: combinatorics proposed, combinatorics



suppose that $\mathcal F\subseteq p(X)$ and $|X|=n$. prove that if $|\mathcal F|>\sum_{i=0}^{k-1}\dbinom{n}{i}$ then there exist $Y\subseteq X$ with $|Y|=k$ such that $p(Y)=\mathcal F\cap Y$ that $\mathcal F\cap Y=\{F\cap Y:F\in \mathcal F\}$(20 points) you can see this problem also here: COMBINATORIAL PROBLEMS AND EXERCISES-SECOND EDITION-by LASZLO LOVASZ-AMS CHELSEA PUBLISHING- chapter 13- problem 10(c)!!!