WOLFRAM|DEMONSTRATIONS PROJECT

Exploring Relations on Sets

​
number of vertices
2
3
4
5
6
7
8
relation
custom
divides
congruent mod 3
a + 2b prime
show
ordered pairs
adjacency matrix
properties
clear edges
Your graph generates the relation
R = {}
A relation
R
on a set
A
is a subset of the Cartesian product
A×A
. The graph of a relation is a directed graph with vertex set
A
and edges determined by the ordered pairs in
R
. This Demonstration lets you explore relations on the set
{1,…,n}
for
n=2
through
n=8
. 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
n
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
R
(the ordered pairs), the adjacency matrix, or the properties of the relation (reflexive, symmetric, antisymmetric, transitive).