Social Networks were created to allow users to maintain circles of friends and acquaintances. Over time, they have come to be used to share data objects such as pictures between friends. There have been several approaches to formalize social networks in order to specify complicated access control policies for such objects. These approaches have involved a combination of existing logic with custom languages, with new operators being introduced when more complex policies needed to be expressed. In this paper we demonstrate that set theoretic notation provides a convenient syntax for specifying a social network and the associated access control policies. We demonstrate that our notation enables us to extend the range of policies that can be articulated. We also demonstrate that our notation is simpler and more concise than existing approaches.