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A subset is a set that contains the same elements from another set, even if not all elements are present as long as all the elements are elements of the set, then you can call that set a subset of that given set.  The subset of a set can be the set itself:
            A = { M, A, T, H}
            B = { A, T, H, M}
Then, B is a subset of A. But, B is not a proper subset of A because it has the same number of elements that A has.

A proper subset is a subset only on which it does not include the same number of elements.
           A = {M, A, T, H}
           B = {A, T. H, M} - subset
          C = { A, T}       - proper subset
          D = { }   - proper subset