Relation Properties Explorer

A relation on a set is just a collection of ordered pairs — arrows between elements. Tap the grid to add or remove pairs, and watch live whether your relation is reflexive, symmetric and transitive, with the exact reason for each. When all three hold, it is an equivalence relation.

Properties

Tap a cell to add or remove the pair (a, b) A loop means a pair like (2, 2) Get all three green for an equivalence relation

Set

Your relation

What each means

Reflexive: every element relates to itself — (a, a) for all a.
Symmetric: if (a, b) is in, so is (b, a).
Transitive: if (a, b) and (b, c) are in, so is (a, c).
All three together → an equivalence relation.