Equivalence Class: FAQs

1. What is the Equivalence Class?

An equivalence class is a subset within a set, formed by grouping all elements that are equivalent to each other under a given equivalence relation. It represents all members that are considered equal by that relation.

2. What is the Symbol for Equivalence Class?

The symbol for an equivalence class is typically written as [a], where “a” is a representative element of the class. This notation denotes the set of all elements equivalent to “a” under a specific equivalence relation.

3. How do you find the Equivalence Class of a Set?

To find the equivalence class of a set, follow these steps:

Step 1: Define an Equivalence Relation.

Step 2: Select an Element from Set.

Step 3: Identify Equivalent Elements to the Selected Elements.

Step 4: Form the Equivalence Class containing all the elements equivalent to the selected element.

4. What is the difference between Equivalence Class and Partition?

Equivalence classes are subsets formed by an equivalence relation, while partitions are non-overlapping subsets covering the entire set. Every equivalence class is a subset in a partition, but not every partition arises from an equivalence relation.

5. What is an Equivalence Relation?

A relation that is reflexive, symmetric, and transitive, dividing a set into disjoint subsets.

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.