How Do You Solve the Second Part of an Equivalence Relations Problem?

MHB
Thread starter loydchase
Start date Nov 17, 2018
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Equivalence Equivalence relations Relations

In summary, an equivalence relation is a mathematical concept that defines a relationship between elements of a set, satisfying three properties: reflexivity, symmetry, and transitivity. To determine if a relation is an equivalence relation, one must check if it satisfies all three properties. Examples of equivalence relations include "is equal to" on the set of real numbers, "is congruent to" on the set of integers, and more. Equivalence relations are used in mathematics to classify objects into different equivalence classes, simplifying and organizing complex problems. They also have various real-world applications, such as identifying similar objects in computer science, grouping objects in data analysis, and categorizing individuals in social sciences.

Nov 17, 2018

loydchase

I understand that the first part of the equation is an equivalence class due to reflexivity, symmetry, and transivity... but I am confused on the second part. Could someone please help me out? THANKS

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Nov 17, 2018

Evgeny.Makarov

Gold Member

MHB

Welcome to the forum!

What exactly is the problem statement?

1. What is an equivalence relation?

An equivalence relation is a mathematical concept that defines a relationship between elements of a set. It is a binary relation that must satisfy three properties: reflexivity, symmetry, and transitivity.

2. How do you determine if a relation is an equivalence relation?

To determine if a relation is an equivalence relation, you must check if it satisfies the three properties of reflexivity, symmetry, and transitivity. If it satisfies all three, then it is an equivalence relation.

3. What are some examples of equivalence relations?

Some examples of equivalence relations include:
- "is equal to" on the set of real numbers
- "is congruent to" on the set of integers
- "is the same age as" on the set of people
- "is the same nationality as" on the set of countries

4. How are equivalence relations used in mathematics?

Equivalence relations are used in mathematics to classify objects into different equivalence classes. This allows for the simplification and organization of complex mathematical problems, making them easier to solve.

5. What are some real-world applications of equivalence relations?

Equivalence relations have various real-world applications, such as:
- Identifying similar objects in computer science
- Grouping objects with similar properties in data analysis
- Categorizing individuals based on shared characteristics in social sciences
- Establishing equivalence classes in economics to compare prices of goods