Example: Set A {1, 2,3} Set B {1, 2,3,4} proper subset, where A is B. If set b {1, 2,3} cannot be proper subset, then it can only be a subset. Generally speaking, some (but not all) elements in set B can be taken out to form a new set A, so this new set A is the proper subset of set B..
Special case: An empty set is the proper subset of any non-empty set.