We say a set is a subset of another set if every element of is also an element of , and we denote this by . The empty set is a subset of every set, and every set is a subset of itself. The notation emphasizes that may be equal to , while says that is any subset of other than itself. In the latter case, is called a proper subset.
The following is a true statement:
The set of all subsets of a given set is called the power set of and is denoted or . The number of subsets of is .