Relation Calculator
Analyze mathematical relations for properties like reflexivity, symmetry, transitivity, and more.
Define Relation
S = {1, 2, 3}
|R| = 4 pairs
Quick Examples
Relation Properties
ReflexiveYES
IrreflexiveNO
SymmetricNO
AntisymmetricYES
TransitiveYES
Classification
Equivalence RelationNO
Reflexive + Symmetric + Transitive
Partial OrderYES
Reflexive + Antisymmetric + Transitive
Total OrderNO
Partial Order + Comparability
Derived Relations
Inverse R⁻¹:
{(1, 1), (2, 1), (2, 2), (3, 3)}
Reflexive Closure:
{(1, 1), (1, 2), (2, 2), (3, 3)}
Relation Properties Reference
Reflexive
Every element is related to itself: (a,a) ∈ R for all a
Symmetric
If (a,b) ∈ R then (b,a) ∈ R
Transitive
If (a,b) ∈ R and (b,c) ∈ R then (a,c) ∈ R