Equivalence relation facts for kids

Kids Encyclopedia Facts

The equivalence relation is a mathematical relation that is symmetric, transitive and reflexive. Using this relation, it is possible to partition a set into (non-empty) subsets, which are called equivalence classes. As an example, look at the animals on a farm: We now define a relation: we say that two animals are related, if they belong to the same species. That way, a cow is related to an ox, but not to a chicken. The relation we just defined is an equivalence relation:

  • It is reflexive: each animal is of the same species as itself
  • It is symmetric: if the cow is the same species than the ox, then the ox is also the same species as the cow.
  • It is transitive: if a cow and a bull, and a bull and an ox are of the same species, they are all of the same species of cattle

In this example, all cattle form an equivalence class.

Equivalence relation Facts for Kids. Kiddle Encyclopedia.