Define the proper and improper subsets?

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.

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.