Let \(W\) be a set with elements \(s\), and consider an initial collection of subsets of \(W\), e.g., the singleton sets \(\{ s \}\). Now consider the operation of taking the complement \(\bar{R}\) of a given set \(R\): the complement \(\bar{R}\) contains exactly and all those \(s\) that are not included in \(R\). Next consider the join \(R \cup Q\) given sets \(R\) and \(Q\): an element \(s\) is a member of \(R \cup Q\) precisely when it is a member of \(R\), \(Q\), or both. The collection of sets generated by the operations of complement and join is called an algebra, denoted \(S\). In statistics we interpret \(S\) as the set of samples, and we can associate sets \(R\) with specific events or observations. A specific sample \(s\) includes a record of the event denoted with \(R\) exactly when \(s \in R\). We take the algebra of sets like \(R\) as a language for making claims about the samples.