Answered: 9.32. A relation Ris defined on the set…

9.32. A relation Ris defined on the set A = {a+bv2: a,b € Q, a + bv/2 + 0} by x R y if æ/y E Q. Show that Ris an equivalence relation and determine the distinct equivalence classes.

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: (b) Is an equivalence relation on Z? If not, is this relation reflexive, symmetric, or transitive?…

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: Let N be the set of all natural numbers and let R be a relation in N, defined by R = {(a, b): a is a…

A: Given Set = set of all natural numbers N Relation = R = { (a,b) : a is multiple of b } A…

Q: In each item below, verify that ~ is an equivalence relation on the given set. Let S = Z × N. Define…

A: Since you have asked multiple questions, we will solve the Question Q (a) and (b) for you. If…

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

Q: Prove that the relation of congruence is an equivalence relation.

A: A relation is said to be an equivalence relation if and only if the relation is reflexive, symmetric…

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: 7. Let (a, b), (c,d) E R2. Define a relation ~on R² by (a, b) (c,d) if 2a - b = 2c-d. (a) Show that…

Q: Let R be the relation on the set of ordered pairs of positive intergers such that (refer to image).

Q: Let S be the relation on the set R^2 defined by (x, y) S (w, z) if |x| + |y| = |w| + |z|. Prove or…

A: Definition of an Equivalence Relations: A relation R on a set A is an equivalence relation if…

Q: 5. Let a and b be real numbers, not both zero. For (71, y1) and (12, 42) in R², set (11, yı) ~ (12,…

Q: A relation ~ is defined on the set of all pairs of integers by the formula (m,n) ~ (u,v) m - An =…

Q: Let R=}(x,y)|2 divides 8x+by} be a relation the Set H= {1, 2,3.4,5, 6. 10 Determine whether the…

Q: properties:Reflexive,Symmetric and Transitive. a R b iff a+b is evenly divisible by 3 b)Does this…

Q: Let A = Z and B = Z\{0}. Show that the relation R on A x B defined by (a, b)R(c, d) if ad = bc, is…

Q: 9. Define a relation R on {-2,-1,0, 1, 2, 3, 4, 5, 6, 7} by a R b if and only if 3a+b is a multiple…

Q: 11. Let A = {1,2,3,4} and B = {A, B, C, D, E}. Consider the following relations and state whether…

Q: artial order relation but not a e, cTd, aTe and eTd. ersi diagram for each possible rela

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: Let I be the set of all straight lines in the plane. Define and equivalence relation R by x R y iff…

A: Let, R be a relation on L(set of all straight lines in the plane) defined as, xRy iff x and y are…

Q: Decide the equivalence classes of the equivalence relation R defined on Z by aRb if 3 | (2a + 7b),…

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: 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: R={(0,4), (3,0), (3,1), (4,2)}. Find transitive closer of R. Show diagram. A=Z+ x Z+ show relation R…

A: The question involves finding the transitive closure of a relation R and demonstrating the relation…

Q: Please show the following question in detail, I don't understand one bit of it, " Let R be a…

Q: 6. Let (a, b), (c,d) E R2. Define a relation ~on R2 by [ (a, b)~ (c,d) if |ab|=|cd| Show that is an…

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: (Chapter 11.4, #3) The relation relation. Sketch it, by drawing Z as a subset of the line, then…

A: The objective is to show that x≡ymod4 is an equivalence relation. To show the relation is an…

Q: Give an example of relation on {1,2,3,4} that is reﬂexive, not symmetric, and not transitive

Q: Let be the relation defined on R by the condition that x - y if x³-y³ = 13(x - y). For example, 1-3,…

Q: Decide whether the following relations is a partial order or not. (a, b) | a Í b, a and b are…

A: We have to decide whether given relation is partial order or not?

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

Q: Let A # 0 be a set. Prove that A? is an equivalence relation on A.

Q: Define: what is an equivalence relation?

Question

9.32. A relation Ris defined on the set A
= {a+bv2: a,b € Q, a + bv/2 + 0} by x R y if æ/y E Q. Show that Ris an equivalence relation and
determine the 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.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Relations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

I need solution of this question
A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd; x ∈ A, y ∈ B}. Write R in roster form.
Find a basis for the space of 2 by 3 matrices whose nullspace contains (2, 1, 1 ).
3. Let R be a relation defined on the set A = N × N where (a, b) R (c, d) if að = cd. Show R is an equivalence relation. Then, list the elements of the equivalence class [(9, 2)].
Show that if for a relation R we know that R^2 ⊆ R, then R is transitive, and conversely.
Provide right answer with complete solution Answer letter C only.
Provide me complete solution of question thanks5
Let S be a nonempty set. Consider the relation ~ on P(S) defined by A ~ B if AUBC = S. Is the relation an equivalence relation? Explain. If yes, identify (no need to justify) the equivalence class of
The relation R on the set of all integer numbers is defined by (x, y) = R_if and only if |x| = [y]. Then, R is an equivalence relation. True False
prove why each relation has or does not have theproperties: reflexive, symmetric, anti-symmetric, transitive. 1) Let A = { set of all people }, relation R: A x A where R = { (a,b) | a,b ∈ A, a is at least as tall as b }
i. Determine whether (~p^(p→q)→~q)is a tautology. ii. Define Cartesian product. iii. List the ordered pairs in the relation R from A = {0, 1, 2, 3, 4} to B = {0, 1, 2, 3}, where (a, b) E R if and only if gcd (a,b) =1 iv. How many relations are there on the set {a,b,c,d} Are the following relations on {0, 1, 2, 3} are equivalence relations or v. partial ordered relation? Explain? {(0, 0), (1, 1), (2, 2), (3, 3)}