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I'm looking for a word to describe the relationship between two sets when set A is neither a subset nor superset of set B. Obviously if a technical term exists, great.

Otherwise, imagine someone has inquired whether set A is related to set B. They are only interested in the subset/superset relationship. I reply by saying that set A is (a subset/a superset/equal to/_???) set B. I'm fine with stripping articles, prepositions, etc off to get a single word.

closed as off-topic by tchrist, Hot Licks, user140086, NVZ, vickyace May 5 '16 at 18:35

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    This is really a math question. If the two sets are not in a subset/superset relationship they may be disjoint (with no common elements), or they may have an intersection of some elements which are common between the two sets. – Hot Licks May 2 '16 at 1:24
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    The sets are incomparable, but, to avoid any misunderstanding, you might have to say incomparable with respect to inclusion. – Andreas Blass May 2 '16 at 1:38
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    You might say the sets are unrelated. – Lawrence May 2 '16 at 1:47
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    I'm voting to close this question as off-topic because it belongs on a Math SE site, not here. – tchrist May 2 '16 at 2:15
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    @tchrist Call off the CPVPV. This is about an English word for a non-inclusional relationship between groups. – deadrat May 2 '16 at 2:17
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If sets A and B do not share any element they are "disjoint sets"

If sets A and B share some elements (their intersection isn't the empty set), then they are "intersecting sets"

https://en.wikipedia.org/wiki/Intersection_%28set_theory%29#Intersecting_and_disjoint_sets

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With respect to the partial order of set inclusion, the sets are incomparable.

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Well, this might be a bit technical, but here's how you'd classify verbally each scenario:

If every element in A is contained in B (but not necessarily vice-versa), A is a subset of B. E.g.: A = {1,2,3} and B = {1,2,3,4,5}

If every element in B is contained within A (again not always vice-versa), A is a superset of B. E.g.: A = {9,8,7,6} and B = {7,6}.

If they are neither subsets nor supersets of each other, the following scenarios are possible:

If sets A and B share no elements, they are known as disjoint or independent. E.g. A = {1,2,3,4} and B = {7,8,9}.

If sets A and B share some elements (their intersection isn't the empty set) but one does not contain all elements from the other, I'm not aware of any special name for the sets -- they're basically just sets, and this is probably the most common scenario given two moderately sized sets of distributed data (hence no real need for a special name, I'm guessing).

  • "Independent" is NOT a synonym for "disjoint". Although.it is a common mistake of students in probability and statistics classes to confuse "disjoint" (aka "mutually exclusive") events with "independent" events, the two concepts are totally different, and mutually exclusive events are hardly ever independent. – bof May 3 '16 at 3:32