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
. 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).