What the example of improper subset?

Answer 1

If you have a set S, the only improper subset of S is S itself. An improper subset contains all elements of S and no others. It is therefore equivalent to S.

For example if S ={1,2,3} then the improper subset is {1,2,3}, and an example proper subset is {1,2}.

Answer 2

An improper subset is a subset that includes all the elements of the original set, as well as the set itself. For example, if we have the set A = {1, 2, 3}, then the set A itself is an improper subset of A because it contains all the elements of A. In set notation, we can write this as A ⊆ A.