A subset means that all elements in one set are elements in another set, and a proper subset means that all elements in one set are elements in another set, but at least one element in one set is not in another set.

Symbolic language: If a∈A and both have a∈B, then AB. If any element of set A is an element of set B, then set A is called a subset of set B. It is written as AB (or BA) and read as "A really contains B" (or "B really contains A").

For example, if A is {1, 2,3} and B is {1, 2,3,4}, then A is a subset of B, but not proper subset.