Any set that has elements that are not in that set.
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It isn't. The empty set is a subset - but not a proper subset - of the empty set.
If all elements of set A are also elements of set B, then set A is a subset of set B.
An improper subset is identical to the set of which it is a subset. For example: Set A: {1, 2, 3, 4, 5} Set B: {1, 2, 3, 4, 5} Set B is an improper subset of Set Aand vice versa.
Because every set is a subset of itself. A proper subset cannot, however, be a proper subset of itself.
This problem can be modeled and tested quite easily. Set A can be [X,Y], subset B [X,Y], and subset A [X,Y]. Therefore A and B are equivalent.