8. Consider the binary relation R defined on (N* x N*) by:V (x1. Y1). (X2, Y2) E N* x N*. (x1, Y1) R (X2. Y2) →x1 < x2 and yı< y2(a) Show that R is an order relation on N* x N*.(b) Determine if the order is total.

Answered: Image /qna-images/answer/04cc3ce4-b59c-4ce5-a8c9-64db7d26b017.jpg

8. Consider the binary relation R defined on (N* x N*) by: V (x1. Y1). (X2. Y2) E N* x N*, (x1. Yı) R (x2, Y2) → X1 < x2 and yı < y2 (a) Show that R is an order relation on N* x N*. (b) Determine if the order is total.

8. Consider the binary relation R defined on (N* x N) by: V (x1. Y1). (X2. Y2) E N x N, (x1. Yı) R (x2, Y2) → X1 < x2 and yı < y2 (a) Show that R is an order relation on N x N*. (b) Determine if the order is total.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 24E: For any relation on the nonempty set, the inverse of is the relation defined by if and only if ....

See similar textbooks

Related questions

Q: A relation R defined on the set of real numbers is such that xRy and yRx = x = y: R is said to be A…

A: There are many types of relations Symmetric Asymmetric Reflexive Transitive

Q: Is the relation R on X is reflexive, symmetric, weakly antisymmetric, antisymmetric, transitive?…

Q: ) Let R = {(a,b) : 3keza = k * b} be a relation over the positive integers. Prove or disprove that R…

A: Given that R=(a,b):a=k*b To show reflexive it is enough to show that a~a. It is true because, a=1*a.…

Q: 7.1.4 A relation is defined on N by a Rb + ; E N. Let c,d E N. Under what conditions is it…

Q: ). Let R be binary relation on N defined by xRy if and only if x- 2s ys x+2. Is R reflexive? Is R…

A: We will usethe definition of reflexive, symmetric, antisymmetric and transitive realtion to answer…

Q: 6. Compute the norms for (a)||f()||, (b) ||F(x)||2, (c)||f(x)||, where f(x) = -V1-r", defined on [0,…

A: Given

Q: Assume that you know that ~ is an equivalence relation on R\ {0} defined as follows: xy > 0. Find…

Q: 5. Let a E G be fixed. Define y: G → G by p(x) = axa-1 for all x E G. Prove that p is a…

A: To find - Let a∈G be fixed. Define ψ:G→G by ψx=axa-1 for all x∈G. Prove that ψ is a homomorphism.

Q: 1. if R and T are anti-symmetric relations on a set A then (R U T) is anti-symmetric relation on

Q: 5. Suppose that f: X →Y and g : Y → Z are bijections. Prove that gof is a bijection and that (go f)-…

A: We will find out the required solution.

Q: Let R= {(a, b): 3keza k* b} be a relation over the positive integers. Prove or disprove thatR is a…

A: A relation R is partial order relation if R is reflexive, antisymmetric and transitive.

Q: Let T₁, T₂, be the following bounded linear operators ¹ T₁(x₁, x2. X3,) = (x₁, X₁, X₁, X₁, ...)…

A: Here, in the question, there are given the bounded linear operators l1→l∞ which are given as…

Q: 6. Give an example of a relation R on A = {-1, –3, –5} such that: (a) R is both symmetric and…

Q: List all the homomorphisms from D5 to Z2 + Z2.

A: There are 4 homomorphism from D5 to Z2+Z2

Q: relation R on Z defined

A: Given, a relation R on Z defined by mRn ⇔ 7|(m − n) for all m, n ∈ Z.

Q: Prove that there is an additive function T : R --> R that is not linear.

A: Let T: V→W be the linear transformation and we it is linear,…

Q: Let - be the relation on R\{0} given by x ~ y if and only if xy is positive. Prove that this is an…

Q: 1. Suppose that the matrix representation of a relation is given by 11 1 1 0 1 1 1 0 0 11 0 0 0 1 MR…

A: A zero-one matrix is the matrix representation of a relation. The zero-one matrix is the matrix Mij…

Q: 1- R1 = {(A, B) E P(X) × P(X)/A S B} 2- R2 = {(A, B) E P(X) × P(X)/AN B + 0} %3D

Q: (4) Let T be the partial order relation on P({1,2,..., 20}) defined by ATB if and only if |A < |B|…

Q: Let R be a relation from A={−1,0,1,2} to B={a,n,i} such that (x,y) provided that x is non-negative…

Q: Consider the Hasse diagram of the following partial order relation P: a b d. f g a) How many maximal…

A: We will be solving Q.3 part (c) and (d) as mentioned. The given Hass diagram of partial order…

Q: 6. Consider the relation R on Z defined by xRy iff x – y= 4n for some n Ɛ Z. (a) Show that R is an…

Q: Suppose R1 is a relation on domain X1 and R2 is a relation on domain X2 Define a new relation R…

Q: ~ on T by (x1, y1, Z1) Let T 3D {(x, у, г) € R'| (х, у, 2) # (0, 0, 0)}. Define ~ on T by (х1, У1,…

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: (b). Let Y = {a, e, o, i, u}, take two relations R and S on Y and Prove that (SoR)-1 : R-1os-1.

A: composition of relations

Q: 4. For r, y E R, let z y if and only if (x- y) E Q. Show that defined as such is an equivale…

A: ~ is defined as : For all, x, y in R, x~y if and only if (x-y) belongs to Q Reflexivity : x~x for…

Q: 4.4.4 List the relation on N defined bv h(x, y) e N x N : x > y } 9 Scanned with CS CamScanner as a…

A: The relation given is already a subset of the Cartesian product N x N. It can be written as follows.

Q: Consider X = [1,2]? with the relation (x1, y1)~(x2, Y2) if x1Y2 = x2y1. Also define 3x g: X → [1,2]…

A: We shall solve first three subparts only as per company's guidelines. For others please post again…

Q: 2|A:k||2|| Bx:||2) < || |||B||F k%3D1

A: Please check the answer in next step

Q: Consider the Hasse diagram of the following partial order relation P: a C f a) How many maximal…

A: A Hasse diagram is a graphical representation of the relation of elements of a partially ordered…

Q: Q1 Given a relation R on Z defined by mRn7|(mn) for all m, n € Z. Find the equivalent class…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Consider the recurrent relation An = 2 An-1 - 1 with initial condition A1 = 3 %3D %3D The…

A: SOLUTION-

Q: Compute the convolution x[n]*h[n] for all n> 0, by using Graphical or Tabular method. x[0] = 3, x[1]…

Q: 1 Recall that for x, y ≤ R, |x − y| ≤ Rf is the absolute value of x - y. That is, if x-y≥0 |x - y =…

A: Please see the below picture for detailed solution.

Q: 2. Let S = {Canada, France, India, Japan, Norway, Philippines, USA} and II(S) = {{Canada, USA),…

A: 1) Let S=Canada, France, India, Japan, Norway, Philippines, USA and ∏S=Canada, USA, France,…

Q: (4) Let T be the partial order relation on P({1, 2,..., 20}) defined by ATB if and only if |A]< |B|…

A: Given T be the partial order relation on P1,2,...,20 defined by ATB if and only if A<B or A=B.

Q: Consider X = [1,2]? with the relation (x1, y1)~(x2, Y2) if x1Y2 = x2y1. Also define 3x g: X → [1,2]…

Q: 3. I Consider the relation R= {(r, y) | x+y is even} on the set Z of integers. Show %3D that R is an…

Q: 1. if R and T are anti-symmetric relations on a set A then (R U T) is anti-symmetric relation on А.

Q: 2. A relation p is defined on the set of all real numbers R by xpy if and only if |x-yl s y, for x,y…

Q: 14. For a,b E Z, define a ~ b if and only if 4a + b is a multiple of 5. Show that defines an…

Q: Let R3 be the relation on Z+ such that xR3y if and only if 2x – 3y > 0. (Recall that Z+ = {1,2,3, 4,…

Q: Q2/(A): Let f: M → N be R-epimophism and K C M . Prove that if KN Ker (f) = (0) , then (f|K): K → N…

A: This problem is related to R-homomorphisms. Given that, f:M → N is a R-epimorphism…

Q: In this exercise, you want to show that a relation RC A? is transitive + R"C R for all n E N = {1,2,…

Q: 40

A: By using the definition of equivalence relation solution is given as follows :

Q: a L4 D 2 of 5 disprove that R is a partial order : {(a,b) : 3keza = k * b} be a relation over the…

Q: 2.4 (34). Let R be a partial order relation on a finite set S. Show that S has a maximal element…

A: Given: Let R be a partial order relation on the finite set S

Question

8. Consider the binary relation R defined on (N* x N*) by:
V (x1. Y1). (X2, Y2) E N* x N*. (x1, Y1) R (X2. Y2) →x1 < x2 and yı< y2
(a) Show that R is an order relation on N* x N*.
(b) Determine if the order is total.

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

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

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

23. Let be the equivalence relation on defined by if and only if there exists an element in such that .If , find , the equivalence class containing.
Prove statement d of Theorem 3.9: If G is abelian, (xy)n=xnyn for all integers n.
For any relation on the nonempty set, the inverse of is the relation defined by if and only if . Prove the following statements. is symmetric if and only if . is antisymmetric if and only if is a subset of . is asymmetric if and only if .
Complete the proof of Theorem 5.30 by providing the following statements, where and are arbitrary elements of and ordered integral domain. If and, then. One and only one of the following statements is true: . Theorem 5.30 Properties of Suppose that is an ordered integral domain. The relation has the following properties, whereand are arbitrary elements of. If then. If and then. If and then. One and only one of the following statements is true: .
In Exercises , prove the statements concerning the relation on the set of all integers. 18. If and , then .
A relation R on a nonempty set A is called asymmetric if, for x and y in A, xRy implies yRx. Which of the relations in Exercise 2 areasymmetric? In each of the following parts, a relation R is defined on the set of all integers. Determine in each case whether or not R is reflexive, symmetric, or transitive. Justify your answers. a. xRy if and only if x=2y. b. xRy if and only if x=y. c. xRy if and only if y=xk for some k in . d. xRy if and only if xy. e. xRy if and only if xy. f. xRy if and only if x=|y|. g. xRy if and only if |x||y+1|. h. xRy if and only if xy i. xRy if and only if xy j. xRy if and only if |xy|=1. k. xRy if and only if |xy|1.
Consider the mapping :Z[ x ]Zk[ x ] defined by (a0+a1x++anxn)=[ a0 ]+[ a1 ]x++[ an ]xn, where [ ai ] denotes the congruence class of Zk that contains ai. Prove that is an epimorphism from Z[ x ] to Zk[ x ].
Describe the kernel of epimorphism in Exercise 20. Consider the mapping :Z[ x ]Zk[ x ] defined by (a0+a1x++anxn)=[ a0 ]+[ a1 ]x++[ an ]xn, where [ ai ] denotes the congruence class of Zk that contains ai. Prove that is an epimorphism from Z[ x ] to Zk[ x ].