# Equivalence Classes Homework Help - #1 & #5

• cgjolberg
In summary, the conversation discusses optional practice problems for an upcoming exam. The problems are available through a link and the person is mainly concerned with problems #1 and #5. They have attempted problem #1 and are unsure about their solution and how to prove it. They also mention that they believe there are four equivalence classes for problem #1. For problem #5, they believe there are 10 equivalence classes and ask for any additional resources or tips. The conversation ends with a mention of a more general solution for problem #5 and a reminder that time is of the essence before the exam.
cgjolberg

## Homework Statement

http://www.math.tamu.edu/~ciken/teaching/spring2014/math302/practice%20midterm%202.pdf
There are several optional problems that have been posted for studying for my exam. I figured it would be easier to read the original than have me try to retype it.
The only ones I am concerned with are #1 and #5

## The Attempt at a Solution

For number one I got the first part just fine.
Would it be 4 equivalence classes? Not sure if I solved it correctly.
Also, how would I go about proving this fact if I got it right.
While of course a proof would be welcome, if you have a link to a resource that would show me how or just any tips really would be great!
For number 5.
Would it be 10 equivalence classes?

Post anything you know. Unfortunately time is of the essence because exam is soon.
Wish this had been posted before:(

Thanks for the help!

Last edited by a moderator:
Your attempt at a solution is a guess? ("would it be 4..."). I guess so.

You can in fact make #5 more general.

x ~ y iff x = y + n*k for some k.

There are n equivalence classes.

For problem 1, let ##|E|## denote the number of edges. Surely there is at least one connected graph for each of ##|E| = 3,4,5,6##. Your solution would imply that there is exactly one equivalence class for each of these values of ##|E|##. Look more carefully at ##|E| = 4##...

Last edited:

## What are equivalence classes?

Equivalence classes are sets that contain elements that are considered equivalent based on a specific criterion or relation. This means that the elements in an equivalence class share a common characteristic or property.

## Why are equivalence classes important in mathematics and computer science?

Equivalence classes are important because they allow us to group related elements together and simplify problems. In mathematics, they are used to define and understand abstract concepts, while in computer science they are used for data classification and algorithm design.

## How do you determine the number of equivalence classes in a set?

The number of equivalence classes in a set is equal to the number of distinct equivalence relations that can be defined on that set. This can be calculated using the Bell numbers formula or by using partitioning techniques.

## Can you give an example of how equivalence classes are used in real-life situations?

One example is in the field of genetics, where individuals are grouped into equivalence classes based on shared genetic traits. This allows for the study of inherited traits and the prediction of genetic diseases.

## How can I approach solving a homework problem involving equivalence classes?

First, identify the equivalence relation that is being used in the problem. Then, determine the elements that belong to each equivalence class. Finally, use the properties of equivalence classes to simplify the problem and find the solution.

Replies
1
Views
2K
Replies
3
Views
2K
Replies
1
Views
2K
Replies
3
Views
2K
Replies
8
Views
7K
Replies
2
Views
4K
Replies
9
Views
3K
Replies
19
Views
1K
Replies
6
Views
2K
Replies
4
Views
6K