No. The empty set has no proper subset. In the case of infinite sets, complications might arise (I am not quite sure about this).
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No. The null set cannot have a proper subset. For any other set, the null set will be a proper subset. There will also be other proper subsets.
The set X is a proper subset of Y if Xcontains none or more elements from Y and there is at least one element of Y that is not in X.
A set with only one element in it. The only proper subset of such a set is the null set.
Proper subset definitionA proper subset of a set A is a subset of A that is not equal to A. In other words, if B is a proper subset of A, then all elements of B are in Abut A contains at least one element that is not in B.For example, if A={1,3,5} then B={1,5} is a proper subset of A. The set C={1,3,5} is a subset of A, but it is not a proper subset of A since C=A. The set D={1,4} is not even a subset of A, since 4 is not an element of A.
The only proper subset of a set comprising one element, is the null set.