What is difference between proper and improper subset? Is Phi a proper subset or not?

An improper subset is a subset containing every element of the original set. A proper subset contains some but not all of the elements of the original set. For example, consider a set {1,2,3,4,5,6}. Then {1,2,4} and {1} are the proper subset while {1,2,3,4,5} is an improper subset.

The empty set i.e phi is a proper subset of any set with at least one element in it and improper subset of phi itself.