Define the proper and improper subsets?

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.

Example: 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.

Answer: A proper subset is one that contains few elements of the original set whereas an improper subset, contains every element of the original set along with the null set.