 Some sets, such as the set of all teacups, are not members of themselves. Other sets, such as the set of all non-teacups, are members of themselves. Call the set of all sets that are not members of themselves “\(R\).” If \(R\) is a member of itself, then by definition it must not be a member of itself. Similarly, if \(R\) is not a member of itself, then by definition it must be a member of itself. 