a characterizing property of its elements, within braces { }. Since sets are objects, the membership relation can relate sets as well. A derived binary relation between two sets is the subset relation, also called set inclusion. If all the members of set are also members of set , then is a subset of , denoted . For example, is a subset of , and so is but is not. As implied by this definition, a set is a subset of itself. For cases where this possibility is unsuitable or would make sense to be rejected, the term proper subset is defined. is called a proper subset of if and only if is a subset of , but is not equal to . Also, 1, 2, and 3 are members (elements) of the set , but are not subsets of it; and in turn, the subsets, such as , are not members of the set . Just as arithmetic features binary operations on numbers, set theory features binary operations on sets. The following is a partial list of them: Union of the sets and , denoted , is the set of all objects that are a member of , or , or both. For example, the union of and is the set . Intersection of the sets and , denoted , is the set of all objects that are members of both and . For example, the intersection of and is the set . Set difference of and , denoted , is the set of all members of that are not members of . The set difference is , while conversely, the set difference is . When is a subset of , the set difference is also called the complement of in . In this case, if the choice of is clear from the context, the notation is sometimes used instead of , particularly if is a universal set as in the study of Venn diagrams. Symmetric difference of sets and , denoted or , is the set of all objects that are a member of exactly one of and (elements which are in one of the sets, but not in both). For instance, for the sets and , the symmetric difference set is . It is the set difference of the union and the intersection, or . Cartesian product of and , denoted , is the set whose members