A subset may include all of the elements or any combination of the elements of the original set including the original set. (A subset notation is a sideways U with a line under it.) Note: the line under the sideways U indicates that all elements including the original set are included in this designation.

A proper subset may include any combination of the elements of the original set but not the original set itself. ( A proper subset notation is a sideways U) Note: the lack of the line under the sideways U in this notation indicates that the original set is not included in this designation.