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I'm having some problems with this problem concerning VC dimensions ( http://en.wikipedia.org/wiki/VC_dimension ), I hope for some helping input.

Given a set $L$ of $n$ lines in the plane, define a hypergraph $H=(L,S)$ such that its vertices are the lines and a subset $l$ of $L$ belongs to $S$ iff there exist points $p$ and $q$ such that all lines in $l$ lie between $p$ and $q$, what is the VC dimension of $H$?

Now, I've managed to show the VC dimension is at least 5, I basically found a group of 5 lines with 4 of them being parrlell to each other with differing lengths and the fifth being perpendicular to the four. but I can't think of a solid proof why it shouldn't be more than 5 (it might be more, its a bit confusing to me).

Thanks a lot.

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I'm having some problems with this problem concerning VC dimensions, I hope for some helping input.

Given a set L $L$ of n $n$ lines in the plane, define a hypergraph H=(L,S) $H=(L,S)$ such that its vertices are the lines and a subset l $l$ of L $L$ belongs to S $S$ iff there exist points p $p$ and q $q$ such that all lines in l $l$ lie between p $p$ and q, $q$, what is the VC dimension of H?$H$?

Now, I've managed to show the VC dimension is at least 5, but I can't think of a solid proof why it shouldn't be more than 5 (it might be more, its a bit confusing to me).

Thanks a lot.

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