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The set {1, 3} is a proper subset of {1, 2, 3}.

The set {a, b, c, d, e} is a proper subset of the set that contains all the letters in the alphabet.

All subsets of a given set are proper subsets, except for the set itself. (Every set is a subset of itself, but not a proper subset.) The empty set is a proper subset of any non-empty set.

This sounds like a school question. To answer it, first make up any set you like. Then, as examples of proper subsets, make sets that contain some, but not all, of the members of your original set.

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