Properties of Equivalence Classes
The properties of equivalence classes are:
- Every element belongs to exactly one equivalence class.
- Equivalence classes are disjoint i.e., intersection of any two equivalence class is null set.
- The union of all equivalence classes is the original set.
- Two elements are equivalent if and only if their equivalence classes are equal.
Read More,
Equivalence Class
Equivalence Class are the group of elements of a set based on a specific notion of equivalence defined by an equivalence relation. An equivalence relation is a relation that satisfies three properties: reflexivity, symmetry, and transitivity. Equivalence classes partition the set S into disjoint subsets. Each subset consists of elements that are related to each other under the given equivalence relation.
In this article, we will discuss the concept of Equivalence Class in sufficient detail including its definition, example, properties, as well as solved examples.
Table of Content
- What are Equivalence Classes?
- Examples of Equivalence Class
- Properties of Equivalence Classes
- Equivalence Classes and Partition