The relation R defined on Z by aRb if 3 | (2a + 7b) is an equivalence relation, I have the equivalence classes but I have no idea how they get them, please explain step by step in detail, I have seen many examples but I really dont get it Let's see what the equivalence classes look like for the equivalence relation definedWe begin with the integer 0. Here,.In addition,[0] = {x € Z: x R 0} = {x € Z: 3|(2x+7.0)}= {x € Z : 3 | 2x} = {x € Z : 3 | x} = {0, ±3, ±6, ...}.For the integer 1,[1] = {x € Z: x R 1} = {x € Z : 3 | (2x+7-1)}= {x € Z: 3 | (2x + 7)} = {1, −2, 4, −5, 7, 8, 10, ...}.[2] = {x € Z: x R 2} = {x € Z : 3 | (2x+7-2)}= {x € Z: 3 | (2x + 14)} = {2, —1, 5, —4, 8, —7, 11, ...}.It turns out that these are the only distinct equivalence classes.

The relation defined on by if is an equivalence relationTo help understanding the equivalence…

The relation R defined on Z by aRb if 3 | (2a + 7b) is an equivalence relation, I have the equivalence classes but I have no idea how they get them, please explain step by step in detail, I have seen many examples but I really dont get it

The relation R defined on Z by aRb if 3 | (2a + 7b) is an equivalence relation, I have the equivalence classes but I have no idea how they get them, please explain step by step in detail, I have seen many examples but I really dont get it

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: 3. Let the relation R on X = {1,3,5, 6, 8, 9, 11} be such that xRy means "x – y is a multiple of 3".…

Q: You just bought a new car from a dealership that sells cars no older than 2015. Consider the…

A: According to the given information, Let S be the set of all cars sold in the period 2015 to 2020.…

Q: (b) Let R be the relation on the set S = {a,b, c, d, e} consisting of the following 6 related pairs…

Q: The relation R defined on Z by aRb if 3 | (2a + 7b) is an equivalence relation. I know the…

A: The objective of the question is to understand how to find the numbers that satisfy the given…

Q: Give a specific reason why the following set R does not define an equivalence relation on the set…

Q: Determine whether the following relation is an equivalence relation? R= {(a, a), (a, c), (c, a), (b,…

Q: is the following relation a functic {(1, 5), (-1, 7), (1, 8), (-4,9)} yes no

A: 1, 5, -1, 7, 1, 8, -4, 9.

Q: 3. Which of the following is an equivalence relation? Explain. (a) lives in the same city as (b) is…

A: Due to Bartleby answering guidelines I have solved only question no 3. Because you didn't mention…

Q: Q4) Let S be the set of registration numbers of students enrolled in a BSCS program in a university…

Q: NXN set on " (a,b)~ (c,d) -) a+d -b+c %3D define d as, equiualence relation? Shaw Is reation ""

Q: Let S be the set of all ordered pairs of non-negative integers. Let R be a relation defined on A…

A: We have to find the equivalence of the given function and we are also given with the set in which…

Q: • Relation "z + y is divisible by 5" on integers z, y is an equivalence relation. Circle the answer:…

A: A relation R is called an equivalence relation if : R is Reflexive, i.e. aRa R is Symmetric, i.e.,…

Q: How can I prove that the relationship r^2 is a subset of r using the definition of composition?

A: The objective of this question is to prove that if r is a transitive relation on a set A, then r^2…

Q: Enter an example of an equivalence relation R on the set X = {0, 1, 2, 4, 8) such that all of the…

A: We need to find an example of an equivalence relation on set X=0,1,2,4,8 such that: 1,4∈R 8,4∉R…

Q: "Let R be the relation defined on Z by aRb if a + b is even. Show that R is an equivalence relation…

Q: 1. In the diagram below, there are 9 points and 8 lines: (a) Let be the relation between the points…

A: Given, In the diagram below, there are 9 points and 8 lines. a) Let ⋄ be the relation between the…

Q: 9. The relation ~ defined on the set of natural numbers by a ~ b means 'a – b is even is : A. an…

A: Equivalence relation : A relation which is reflexive, symmetric and transitive is an equivalence…

Q: Decide whether each of the following relations is an equivalence relation or not. {(a, b) | gpa of…

A: To prove equivalence relation, we have to prove that (i) the relation is reflexive, (ii) the…

Q: Problem 3 Let R be the relation on the set of ordered pairs of positive integers such that ((a, b),…

Q: Determine whether the given relation is an equivalent relation on {1,2,3, 4, 5}. If the relation is…

A: Equivalence class of an element a is given by [a] such that [a]={b:(a, b) lies in R}

Q: A relation is an equivalence relation if it satisfies three properties. which of the following…

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: For every element r in A, there is an element y in B such that (x, y) is in F. Can you please…

A: Relation: The relation from a set A to a set B is a subset of Cartesian product A×B. Function: The…

Q: 4. For each relation R below, determine whether it is an equivalence relation on the given set A.…

A: Definition (Equivalence relation): A relation R is said to be an equivalence relation on a set A if…

Q: Let R be the relation defined on Z by aRb if a + b is even. I have the following equivalence classes…

Q: Give an example of two equivalence relations R and S on the set A = {1, 2, 3} such that RUS is not…

A: 6 Given set is A=1,2,3. Consider the relation R and S on A is given by R=1,1,2,2,3,31,2,2,1 And…

Q: Indicate which of the following relations is an equivalence relation or is a partial order relation.…

Q: Let A = {0,1, 2} × {0, 1, 2, 3}. We define an equivalence relation R on A by saying that (a, b)R(c,…

Q: The relation R defined on Z by aRb if 3 | (2a + 7b) is an equivalence relation. the equivalence…

A: The objective of the question is to understand how the equivalence classes for the given equivalence…

Q: Define a relation Ton the set of real numbers as follows: Vx, y ≤R, x Ty ⇒xy < 0 The relation is not…

Q: Please answer the part (B). I have got a solution for the question on this platform but the answer…

Q: d) ((f g)| for some CEZ, for all xE Z, f(x) – g(x) = C} e) {f, 8) | f(0) = g(1) and f(1) = g(0)}

A: Part (d) From the given information: The relation is . Here, C is constant.

Q: (c) The reversed relation R is an equivalence relation. (d) So R is an equivalence relation if and…

A: (c) If R is an equivalence relation in a set X, then it is reflexive, symmetric and transitive.

Q: Exercises 1-10, determine whether the given relation is an uivalence relation on (1, 2, 3, 4, 5). If…

Question

Let's see what the equivalence classes look like for the equivalence relation defined
We begin with the integer 0. Here,
.
In addition,
[0] = {x € Z: x R 0} = {x € Z: 3|(2x+7.0)}
= {x € Z : 3 | 2x} = {x € Z : 3 | x} = {0, ±3, ±6, ...}.
For the integer 1,
[1] = {x € Z: x R 1} = {x € Z : 3 | (2x+7-1)}
= {x € Z: 3 | (2x + 7)} = {1, −2, 4, −5, 7, 8, 10, ...}.
[2] = {x € Z: x R 2} = {x € Z : 3 | (2x+7-2)}
= {x € Z: 3 | (2x + 14)} = {2, —1, 5, —4, 8, —7, 11, ...}.
It turns out that these are the only distinct equivalence classes.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Question Description

VIEW

Step 2: Finding equivalence classes of given equivalence relation

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 36 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Advanced Math (UPVOTE WILL BE GIVEN. PLEASE WRITE THE COMPLETE SOLUTIONS. NO LONG EXPLANATION NEEDED. CHOOSE THE CORRECT ANSWER. PLEASE ANSWER ALL. SUBQUESTIONS.)
*NOTE: it says "Let A be a nonempty a set". It does not specify what kind of set, so we may NOT assume it is a relation. Thus A^2 means A x A, NOT composition of relations.*
Question 2 List all possible equivalence relations on the set {1,2,3,4} without repetition up to isomorphism. Justify your answer.
I need help answering the attached question. Thank you
The relation R defined on Z by xRy , x + 3y is even is an equivalence relation. Explain step by step why the following are the equivalence classes, please elaborate each step, I don't get what is being done and how, how do you determine when to stop? how do you determine the variables in the bracket? thank you in advance.
Exercise 1.5.5. (a) Why is A- A for every set A? (b) Given sets A and B, explain why A - B is equivalent to asserting B- A. (c) For three sets A, B, and C, show that A- B and B - C implies A - C. These three properties are what is meant by saying that - is an equivalence relation.
For every element r in A, there is an element y in B such that (x, y) is in F. Can you explain how does this differ from a relation? Please answer this in a couple sentences NO NEED TO SHOW PROOF! AGAIN NO PROOF PLEASE!!!
Determine whether the given relation is an equivalent relation on (1, 2, 3, 4, 5} If the relation is an equivalence relation, list the equivalence classes (x, y E {1,2, 3, 4, 5} . ) 3, 4, 5}. 1. {(1,1), (2, 2) , (3, 3) , (4, 4) , (5, 5) , (1, 3) , (3, 1)} 2. {(x, y) | 3 divides x + y}
i need complete solution step by step
Discrete math: please solve both parts 100% accurate
I am having trouble working thru this problem, any help would be appreciated.