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The relation " A is not included in B" OR " B is not includde in A" is the relation of distinction ( non-identity).

Does the relation : " reciprocal non inclusion" have a name?

It cannot be disjunction. For, surely two disjoint sets satisfy this relation, but this is not a necessary condition two sets to be disjoint to satisfy the relation in question.

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Such sets are called incomparable.

In general, this term applies for any partial order $\prec$ when you have $x$ and $y$ such that neither $x\prec y$ nor $y\prec x$ are true.

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  • $\begingroup$ @MatthewDaly.- Now that you say it, I say : " of couse"! $\endgroup$ – user654868 Nov 17 '19 at 17:09
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    $\begingroup$ @EleonoreSaintJames It's nice to know that sometimes I get to be the person who knows the word instead of the person who can't think of the word. ^_^ $\endgroup$ – Matthew Daly Nov 17 '19 at 17:12

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