  For example, if \(R\) is the relation of being a brother, and \(R'\) is the relation of being a parent then \(R \circ R'\) is the relation of being an uncle, (because \(w\) is the uncle of \(v\) iff for some person \(u\), both \(w\) is the brother of \(u\) and \(u\) is the parent of \(v)\). A relation may be composed with itself. For example, when \(R\) is the relation of being a parent, then \(R \circ R\) is the relation of being a grandparent, and \(R \circ R \circ R\) is the relation of being a great-grandparent. It will be useful to write ‘\(R^n\)’, for the result of composing \(R\) with itself \(n\) times. So \(R^2\) is \(R \circ R\), and \(R^4\) is \(R \circ R \circ R \circ R\). We will let \(R^1\) be \(R\), and \(R^0\) will be the identity relation, i.e. \(wR^0 v\) iff \(w=v\).