English edit

 
Euler diagram showing A is a proper subset of B,  AB,  and conversely B is a proper superset of A.

Noun edit

proper subset (plural proper subsets)

  1. (set theory) a set that is a subset of the set, but not equal to it.
    {2, 4, 5} is a proper subset of {1, 2, 3, 4, 5}, but {1, 2, 3, 4, 5} is not.

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