Answered: Consider the relation ? = {(1,1),…

Consider the relation ? = {(1,1), (1,3), (2,2), (3,1), (4,4)} on the set {1,2,3,4}. Find the reflexive closure of ?. Find the symmetric closure of ?. Find the transitive closure of R

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: For the relation R closure of R. {(1,2), (1,4), (3,3), (4, 1)} find (i) R2 (ii) R3 and (iii)…

A: The given relation,

Q: Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}. Choosethe correct…

A: Given : Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}. Choosethe…

Q: 1. The following subsets A, B, and C of R XR are relations on R. Sketch the set. (i) B = {(x, y):…

Q: Let R be the relation on the set A = [1,2,3] containing the ordered pairs (1,3), (2,1), (2,2), and…

A: Given that Let R be the relation on the set A = { 1 , 2 , 3 } containing the ordered pairs (1,3) ,…

Q: Give an example of a relation on the set {a, b, c, d} which is symmetric and transitive, but not…

A: Any relation R from a set Ato A is reflexive if and only if for every x∈A , the pair (x,x)∈R Any…

Q: Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9} and let R be the relation {(a,b) ! a , b} Find the smallest…

Q: Select all pairs in the reflexive closure of the relation R, defined on the set A = { a, b, c, d }…

Q: Suppose that R is the relation that is represented by the following digraph ... a O True O False b d…

A: The objective is to determine whether the directed graph with the relation is a partial order or…

Q: (a) Ri (b) R2= {(1,2), (1,3),(1,4),(2,2),(3,3),(5,3),(5,4),(5,2)} /hich of them is an equivalence…

A: Any relation is equivalence relation if satisfy the following conditions where is set of elements a)…

Q: Given that T is a relation on the set {1, 2, 3, 4}, and the set of ordered pairs is: T = {(1, 1),…

Q: Let R = {(1, 2), (2, 3), (2, 4)} be a relation on {1, 2, 3, 4). a. Show that R is not transitive. b.…

Q: Let S be the set of ordered pairs of positive integers, and define (a,b) R (c,d) to mean that 2a-d =…

A: A relation R is transitive on a set A if xRy and yRz then xRz for all x,y and z belong to A. Now,…

Q: What is the reflexive closure of the relation R = {(a, b) | a > b} on the set of integers? Select…

A: Reflexive Relation Definition: A reflexive relation is the one in which every element maps to…

Q: Indicate whether the relation is: •Reflexive, anti-reflexive, or neither •Symmetric,…

Q: Let A = {a, b, c, d}. How many relations defined on A are re-flexive, symmetric and transitive and…

A: The objective of this question is to find the number of relations defined on set A that are…

Q: Let R = { ( a, b ), ( a, d ), ( b, d ), ( c, a ), ( c, c ), ( d, b ), ( d, c ) } be a relation on…

A: Given: R=a,b,a,d,b,d,c,a,c,c,d,b,d,c The relation R2 contains all ordered pairs (x, z) if (x, y)…

Q: The general solution of y -4y +8y 0 is: Select one: a. c,e 2cos4t + c,e 2sin4t O b. -4t Cze Ce 41+…

A: Given differential equation is y" - 4y' + 8y = 0

Q: Given that T is a relation on the set {1, 2, 3, 4}, and the set of ordered pairs is: T = {(1, 1),…

A: Reflexive: If every element in set A is related to itself, i.e., (a, a) ∈ R for every a in…

Q: Which of the following relations is the Symmetric relation over the set A= {3,5,13}…

Q: Select the correct statement(s) for the relation R, defined on the set A = { a, b, c, d, e } by R=…

Q: 1. Let & be the relation of (a,b) la #b] on the set of integers. What is the reflexive closure of R?

A: As per our company guideline we are supposed to answer only one question with its 3 subparts. Here…

Q: Define relations R₁, ..., R₁ on {1, 2, 3, 4} by R₁ = {(2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3,…

Q: The following definitions are used: a relation on a set A is defined to be irreflexive it, and only…

A: The given set is A=01,2,3 The given relation is R=0,0,0,1,0,2,1,2. (i) Using the definitions of…

Q: For non empty binary relation R={(a, a).(a, b).(a, e).(b, b).(b, e).(c, C).(c, d).(d, d).(e, e)} on…

Q: Give an example of a nonempty relation R on A = {1, 2, 3, 4} which is a. symmetric and transitive…

Q: Consider the relation R ={(1,2),(1,4),(2,1),(2,2),(3,2), (3,4),(4,1)} on the set {1,2,3,4}. Find the…

Q: Let R be the relation on the set (0, 1, 2, 3} and R= {(0, 1), (1, 1), (1, 2), (2, 0), (2, 2), (3,…

Q: Consider the relation ? = {(a, b), (a, d), (b, a), (c, d)} on the set {a, b, c, d}. a. Find the…

Q: The relation R= {(1,1),(1,4),(2,3),(2,4),(3,1),(3,4)} on the set {1,2,3,4} is : Select one: O a. not…

Q: Let R be the relation on the set {1,2,3,4} containing th (1,2), (1,4), (2,1), (2,2), (2,3), (3,1),…

Q: Let A = {a, b, c, d} and let R = {(a, a), (a, b), (a, c), (a, d), (b, b), (b, c), (b, d), (c, c),…

A: Given that be a relation on the set Reflexive: For every…

Q: What is the reflexive closure of the relation R = {(a , b) I a < b} on the set of integers

Q: It is based upon properties of relations. *Explanation is mandatory. Check whether the following…

Q: Consider relation R={(1,1),(1,2),(2,1),(2,2),(3,3)} on the set{1,2,3}. R Is ? Select one: O a. Ris…

A: Let R be a relation defined as . The relation, R is reflexive, if , . The relation, R is…

Q: Using the relation {(1, 2), (1, 4), (3, 3), (4, 1)}, write the relations that have the minimum…

A: Relations are an essential concept in mathematics that describe the connections or associations…

Q: Consider the relation R = {(1,1);(2,3);(3,5);(4,7)}. a. Prove that R is a function from {1,2,3,4}…

Question

Consider the relation ? = {(1,1), (1,3), (2,2), (3,1), (4,4)} on the set {1,2,3,4}.
Find the reflexive closure of ?.
Find the symmetric closure of ?.
Find the transitive closure of R

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 3

VIEW

Step by step

Solved in 3 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

. Let R1, R2, R3 be relations on { a, b, c, d, e }. Find the transitive closures, given their definitions below. i) R1 = { (a, c),(b, d),(c, a),(d, b),(e, d) } ii) R2 = { (b, c),(b, e),(c, e),(d, a),(e, b),(e, c) } iii) R3 = { (a, b),(a, c),(a, e),(b, a),(b, c),(c, a), (c, b),(d, a),(e, d) }
R= {(1,2), (1,3), (1,4), (2,3), (2,4), (3,4)} is a relation on the set A = {1, 2, 3, 4}. 3.a. Show the digraph of R. 3 b. Show the matrx of R. 3.c. Determine whether R is reflexive, symmetric or transitive. You must give reasons for these answers. 100%
Let ? = {1, 2, 3, 4, 5, 6, 7} and define a relation ? ⊆ ? × ? by? = {(1,1), (1,2), (1,3), (2,3), (7,1), (7,2), (7,3), (4,5), (4,6), (5,6), (5,5)}Determine (yes or no) whether ? has the following properties (no justification is required).
Consider the relation R = {(1,3), (1,4), (2,1), (2,2), (3,2), (3,4), (4,1)} on the set {1,2,3,4}. Find the reflexive closure of R. b. Find the symmetric closure of R. C. Find the transitive closure of R.
Let A={1,2,3,4}, B={1,3}, and the relations R1: a
Pls write clearly
Let P={1.2,3,4,12,36} and the relation set R={(1,1) ,(2,2),(3,3),(4,4),(12,12),(36,36),(1,2),(1,3),(1,4),(1,12),(1,36),(2,4)(2,12),(2,36),(3,12),(3,26),(4,12),(4,36)}. Show that (P,R) is a poser. Represent the relation using the diagraph and then draw the Hasse diagram.