S is a proper subset of T if
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You cannot. They are two disjoint subsets of rational numbers.
If A is a subset of B, then all elements in set A are also in set B. If it is a proper subset, then there are also elements in B that are not in A.
A mixed number is a combination of an integer and a proper fraction.
If set A is a subset of set B, that means that all elements in set A are also in set B. In the case of a proper subset, there is the additional specification that the two sets are not equal, i.e., there must be an element in set B that is not also an element of set A.
In an improper fraction the absolute value of the numerator (the top) is bigger than the absolute value of the denominator. An improper fraction is also called a top-heavy fraction.