Two-part question: Let R be a relation from X to Y and S be a relation from Y to Z. Prove or disprove if R and S are surjective, then so is S of R, and prove or disprove if the composition of S of R is surjective, then so is S.

Two-part question: Let R be a relation from X to Y and S be a relation from Y to Z. Prove or disprove if R and S are surjective, then so is S of R, and prove or disprove if the composition of S of R is surjective, then so is S.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 20E: Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not...

See similar textbooks

Related questions

Q: 2) Let Q = {0,1,2,3} and define relation R on Q as follows: R = {(0,0), (0,1), (0,3), (1,0), (1,1),…

Q: 0,1,2

Q: Let R be a relation from Q to Q defined by R = {(a,b): a,b ∈ Q and a – b ∈ Z}. Show that:(i) (a,a) ∈…

A: i) Given that a ∈ Q a-a=0 ∈ Z So, (a,a) ∈ R for all a ∈ Q (proved)

Q: {0, 1, 2, 3, 4, ...} and define the relation - on A by: x~y if x – y is divisible by 3 Determine…

Q: Let R be the relation defined on Z by aRb it a+b is even Find the number of distinct classes? Select…

A: aRb if and only if a+b is even. a and b are integers. Hence, Either a and b both are even or both…

Q: Let R = { (1,1), (3,1), (2,1),(2,2), (1,3) } be a relation on the set A = {1,2,3}. (a) Determine…

A: Explanation of the answer is as follows

Q: Let X = {6, 7, 8, 9} and let the relation R on X be given by R = {(x, y): 3z e N₂ x + z = y}, where…

Q: Let A = {6, 9} , R relation on A defined R by. %3D R = {(a, b): a +2 = b -1 ,a, b E A}. Write R. %3D

Q: Let A = {1,2,3}, X = {1,3}, and R is a relation on A, such that R= {(x,y) | x<y^x, y = A} R"X =…

Q: 1. Let R and S be equlvalence relations on a set A; recall that by definition R, SCAXA. Prove that…

A: We have to solve given problem:

Q: 2. The relations below are defined on the set {0,1,2,3}. Determine which of these relations are…

Q: 3. Let R and S be relations on a set A then (SoR)-1 = R-1o s-1.

Q: Let R be the relation defined by x R y =x<y° Determine if R is an order relation on N? on Z? Justify…

Q: c. Ris a relation on Z such that (x, y) e R if and only if xy 2 0. d. Ris a relation on Z* such that…

Q: Consider the relation R on the set {a,b,c,d,e,f} which is defined as follows: R={(a,a), (a,b),…

Q: 3. Let R be the relation defined on P({1,..., 100}) by ARB if and only if |AU B| is even. Is R…

Q: Let X = {6, 7, 8, 9) and let the relation R on X be given by R = {(x, y): 3 z e N₁ x + z = y}, where…

Q: R.5. Define a relation < on the set of ordered pairs of real numbers (x, y) as follows:…

Q: 3. Let R be a relation defined on Q by: Ga) ER if ad = bc a) Show that R is an equivalence relation…

Q: Given R = { (x,y) ϵ R | (x+y) divides 3 with zero remainder, x,y ϵ A } on A = {1, 2, 3, 4, 5}, which…

Q: Let us define a relation S on R3: If p1 = (x1, y1, z1) and p2 = (x2, y2, z2) are two points in R3,…

Q: Why

A: The given relation R={(3,3),(4,4),(6,6),(7,7),(3,6),(6,3),(4,7),(7,4)}

Q: B. Let A = {1, 2, 3, 4}. Let R be the relation on A defined as follows: R = {(1, 1), (1, 2), (1, 3),…

Q: Let U be the Universal set. Consider the relation S on P(U) (the power set of U) given by: S= {(A,…

A: S is reflexive, transitive but not symmetric.

Q: 1) Let R be the relation on Z+ such that (p, q) R(r, s) if and only if p- s = q ·r. That is, the…

Q: b) Let S = { (x, y) | x, y € R} and relation R on S defined by (x,y) R (p,q) if and only if x-p =…

A: We have S=x,yx,y∈R x,yRp,q if and only if x-p=y-q Reflexive property: A relation R is said to be…

Q: R.5. Define a relation < on the set of ordered pairs of real numbers (x, y) as follows: (X:V1)< (x2,…

A: The relation ≺ is defined as follows: x1,y1≺x2,y2 if and only if x1<x2 or x1=x2 and y1≤y2

Q: Part II: Prove/Disprove the following 2. Let R be the relation on Z, defined as follows: Vm, n e Z,…

Q: b) For a set X = {1, 2, 3, 4}, let P be the partition {{1,3}, {2, 4}}. The partition P induces a…

Q: Given R = { (x,y) ϵ R | x = (y+1), x,y ϵ A } on A = {1, 2, 3, 4, 5}, which of the following…

Q: 3. Let S = R × R and R be the relation on S defined by (a, b)R(c, d) iff a+c=b+d. Determine whether…

A: Reflexive: (x,y) R (x,y) As x+y=x+y Symmetric : if (a,b)R(c,d) then a+b=c+d. Since c+d=a+b then…

Q: Let R be the relation on R defined by Ry if and only if ry 1. Thus R can also be represented as (r,…

A: (a) Obtain the composite relation as follows.

Q: 3. Let R and S be relations on a set A then (SoR)-1 = R0S1.

Q: 4- The orthogonal relation is A: symmetric and reflective relation B: symmetric and not reflective…

Q: f relations R and S on Z such that (a) Both R and S are not equivalence relations but R + S is. (b)…

Q: Let A = {1,2,3, 6}. Define a relation R on A as follows: %3D xRy if y – x > 0 Write out the relation…

A: We have to find the relation R.

Q: y if and only if x < 3y. Determine, plem B4: Consider the relation ~ on N defined by, x ~ proof,…

A: Given the relation ~ on ℕ defined by x~y if and only if x≤3y. 1) Reflexive: For any x∈ℕ, the…

Q: (a) Let U be the Universal set. Consider the relation S on P(U) (the power set of U) given by: S=…

A: Given - S=A,B:(A,B∈P(U)∧(A⊆B) We have to prove properties of reflexivity, symmetry and transitivity…

Q: B. Let A = {1, 2, 3, 4}. Let R be the relation on A %3D defined as follows: R = {(1, 1), (1, 2), (1,…

A: Find if the given relation is reflexive, symmetric or antisymmetric.

Q: 6. Prove the following statements and provide an illustration to substantiate the proof. a) Let R1…

A: (i), (ii) & (iii) implies R1 intersection R2 is an equivalence relation.

Q: 13. Let R C R XR with {(x, y)|x2 =, y?}. Characterize R in terms of whether it is reflexive,…

Q: (a) Explain what it means for a relation R on a set S to be (i) reflexive; (ii) symmetric; (iii)…

Q: 3. Let R be the relation defined by x R y + x² <y? Determine ifR is an order relation on N? on Z?…

Q: (a) Let R be the relation on Z defined as follows: For a, b € Z, a~b if and only if a is a multiple…

A: a) R be the relation on ℤ defined as follows: a,b∈ℤ, a~b if and only if 'a' is a multiple of…

Q: Prove or disprove: 1. For any relations R and S, ran(S • R) = ran(S). 2. If R and S are equivalence…

Q: math question Let the relation R on X = {1, 3, 5, 6, 8, 9, 11} be such that xRy means “x − y is a…

Q: Give examples of relations R and S on Z such that (a) Both R and S are not equivalence relations but…

A: (a) Let R and S be two relations on ℤ such that both R and S are not equivalence relations. Let…

Q: Let A = (0, 1, -1, 2} , R relation on A defined by R = {(a, b) : b= a², a, bE€ A}. Write R. %3D

A: Given , Let A = {0 , 1 , -1 , 2} R relation on A defined by R = {(a , b) : b = a2 , a , b € A} We…

Question

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 3 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

Find mappings f,g and h of a set A into itself such that fg=hg and fh. Find mappings f,g and h of a set A into itself such that fg=fh and gh.
6. a. Give an example of mappings and , different from those in Example , where is one-to-one, is onto, and is not one-to-one. b. Give an example of mappings and , different from Example , where is one-to-one, is onto, and is not onto.
7. a. Give an example of mappings and , where is onto, is one-to-one, and is not one-to-one. b. Give an example of mappings and , different from example , where is onto, is one-to-one, and is not onto.
Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.
Does the relation is a brother of have a reflexive property consider one male? A symmetric property consider two males? A transitive property consider three males?
Label each of the following statements as either true or false. Let R be a relation on a nonempty set A that is symmetric and transitive. Since R is symmetric xRy implies yRx. Since R is transitive xRy and yRx implies xRx. Hence R is alsoreflexive and thus an equivalence relation on A.
Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide whether or not is an equivalence relation. Justify your decision.