Define \(R\) by \(a R b\) if and only if \(a < b\), for \(a, b \in S\). We can visualize the above binary relation as a graph, where the vertices are the elements of S, and there is an edge from \(a\)...Define \(R\) by \(a R b\) if and only if \(a < b\), for \(a, b \in S\). We can visualize the above binary relation as a graph, where the vertices are the elements of S, and there is an edge from \(a\) to \(b\) if and only if \(a R b\), for \(a b\in S\). \( \forall a,b \in S\), if \( a R b \) then \(b R a\), in other words, \( \forall a,b \in S, a R b \implies b R a.\) Define \(R\) by \(a R b\) if and only if \(a \mid b\), for \(a, b \in \mathbb{Z}\).
