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Is there a word that means "Mutually exclusive and collectively exhaustive" (as an adjective) or "to be mutually exclusive and collectively exhaustive" (as a verb), or is there a noun that describes some set as "mutually exclusive and collectively exhaustive?"

For example,

In a good multiple-choice survey item, the answer choices should [be] ____.

The term "shattering" (e.g. the answer choices "shatter" the space of possible answers) was introduced to me as having this meaning, but I don't think that introduction to the term was quite right in accurately conveying the meaning - I now understand that it's a family of functions which can be said to "shatter" a set of points if some function within that family can exactly separate any subset of the points from the rest.

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You might try Partition:

a grouping of the set's elements into non-empty subsets, in such a way that every element is included in one and only one of the subsets.

It seems a bit awkward, but you might try...

In a good multiple-choice survey item, the answer choices should partition the possible answers.

  • Yup, that's the answer. – Drew May 24 '16 at 1:51

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