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Or is this only true for downsets? Thanks!

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    $\begingroup$ could you restate the question in the text, I'm not sure I understand $\endgroup$
    – Asinomás
    Jun 3, 2014 at 20:26
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    $\begingroup$ What's "downsets"? $\endgroup$
    – Asaf Karagila
    Jun 3, 2014 at 21:05

1 Answer 1

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No, for example if $A$ and $B$ have an empty intersection.

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