Exploring Relations on Sets

A relation on a set is a subset of the Cartesian product . The graph of a relation is a directed graph with vertex set and edges determined by the ordered pairs in . This Demonstration lets you explore relations on the set for through . Three specific relations ("divides", "congruent mod 3", and "a + 2b is prime") are included. When using the custom option, a "ghost" of a complete graph on vertices (with loops) appears. Clicking the ghost edges/loops adds edges/loops to the graph and adds the corresponding ordered pairs to your relation. Clicking an edge a second time changes its direction; clicking a third time makes that edge bidirectional. You can view (the ordered pairs), the adjacency matrix, or the properties of the relation (reflexive, symmetric, antisymmetric, transitive).