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I'm interested in formalising/documenting a program plotting Venn charts (well UpSet plots actually). Is there a term that can unambiguously refer to the coloured partition of the visualisation below (obtained from Wolfram alpha from $A \cap B \setminus C$) in relation to $A$ and $B$? It was previously referred to as distinct intersection of $A$ and $B$ (because it does not include the intersection of $A$ and $B$ with any other set) - is there a formal term for this concept?

set overlap illustration

Edit: in general I am interested in a case of $n$ sets. I am looking for a generic name for a region of an intersection of $k$ sets ($k \leq n$) such that it is exclusive to the sets forming the intersection this is it excludes overlap with any other set that do not for this $k$ intersection.

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    $\begingroup$ $(A\cap B)\setminus C = A\cap (B\setminus C)$, so the expression is technically unambiguous. It is still bad form in my opinion to write this without parentheses since it is not immediately apparent to a beginner that this should be the case. $\endgroup$
    – JMoravitz
    Dec 18 '20 at 17:59
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    $\begingroup$ As for if there is a specific name for that set or operation... none that I am aware of beyond the obvious "intersection of $A,B$ and $C^c$" or "Intersection of $A$ and $B$ without $C$" etc... I hesitate to say something like "The region simultaneously occupied by $A$ and $B$ and no others" in general because the image only alludes to the additional set $C$ but does not preclude there existing other unpictured sets which may also occupy a portion of that region. $\endgroup$
    – JMoravitz
    Dec 18 '20 at 18:05
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No, there is not any commonly used term for this. Simply writing it as $(A\cap B)\setminus C$ or $A\cap B\cap C^c$ (with ${C}^c$ referring to the complement of $C$) would be a reasonable choice. If you want to refer to it in words, you could say something like "the region that is in $A$ and $B$ but not $C$", or "the intersection of $A$ and $B$ and the complement of $C$". You could also say something like "the region that is only in $A$ and $B$". I would strongly recommend against "distinct intersection"; that's not the way "distinct" is normally used in mathematics.

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  • $\begingroup$ Thank you. I like distinct because it is a single word that can be used as an argument value in a programming implementation that I am preparing here to achieve a result demonstrated there. Would you recommend a different choice of up to three words for a general case? Should I edit my question to reflect that I am interested in a general case of n sets, and the A, B, C are just examples? $\endgroup$
    – krassowski
    Dec 19 '20 at 0:50
  • $\begingroup$ I'm thinking about this region as being a partition of $A \cap B$ that is exclusive to $A$ and $B$ but I am afraid of using exclusive either as it has yet another meaning in set theory. $\endgroup$
    – krassowski
    Dec 19 '20 at 0:56
  • $\begingroup$ "Exclusive" is a reasonable choice. I don't think there's any single word you can use and expect people to understand what you mean without seeing at least one example. $\endgroup$ Dec 19 '20 at 1:01
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    $\begingroup$ Another word you might use is "exact", to indicate you are listing exactly the sets that your region is in. $\endgroup$ Dec 19 '20 at 1:02

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