Practice Problems on Equivalence Class
Problem 1: aRb if a+b is even. Determine if it’s an equivalence relation and its properties.
Problem 2: xSy if x and y have the same birth month. Analyze if it’s an equivalence relation.
Problem 3: Consider A = {2, 3, 4, 5} and R = {(5, 5), (5, 3), (2, 2), (2, 4), (3, 5), (3, 3), (4, 2), (4, 4)}. Confirm that R is an equivalence type of relation.
Problem 4: Prove that the relation R is an equivalence type in the set P= { 3, 4, 5,6 } given by the relation R = { (p, q):|p-q| is even }.
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
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