Playground

Relation Checker

Define a relation on a set and check whether it's reflexive, symmetric, transitive, etc. — and whether it forms an equivalence relation or partial order.

R \subseteq A \times A

Definition

Universe A (comma-separated)

Pairs (one per line, format (a, b))

A = {0, 1, 2, 3, 4, 5} · |A| = 6 · |R| = 12

Properties

Reflexiveyes

∀a∈A. (a,a)∈R

Irreflexiveno

∀a∈A. (a,a)∉R

Symmetricyes

(a,b)∈R ⇒ (b,a)∈R

Antisymmetricno

(a,b),(b,a)∈R ⇒ a=b

Transitiveyes

(a,b),(b,c)∈R ⇒ (a,c)∈R

Totalno

∀a,b∈A. (a,b)∈R ∨ (b,a)∈R

Classification

EQUIVALENCE RELATION

Reflexive+Symmetric+Transitive ⇒ Equivalence. Reflexive+Antisymmetric+Transitive ⇒ Partial order.

Relation matrix

	0	1	2	3	4	5
0	1	0	0	1	0	0
1	0	1	0	0	1	0
2	0	0	1	0	0	1
3	1	0	0	1	0	0
4	0	1	0	0	1	0
5	0	0	1	0	0	1