$\mathcal F \subset 2^X$, where $ X = \{1\ldots n\} $ and $ \forall F_1, F_2 \in \mathcal F$ : |$F_1 \cap F_2 $| $ \neq 0$. I need to find the amount of such $\mathcal F$ such that |$\mathcal F$| = $2^{n-1}$. Can anyone help?
$\mathcal F\subset 2^{[n]}$ and $\forall F_1, F_2\in\mathcal F : |F1∩F2| \neq0$. What is the amount of $\mathcal F : |\mathcal F| = 2^{n−1}$?
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discrete-mathematics
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0*Advice*: Try to solve your problem first when $\,n=1,2,3\,$... – 2012-11-27