Ris said to be.reflexivesymmetrictransitiveAll of the choicesNone of the choicesRis said to berelated to c.symmetrictransitivereflexiveAll of the choicesNone of the choices.transitiveif a is related to a for all a € S. *The relation R={(1,2),(2,1),(3,2), (2,3)) on set A=(1,3,3) is ___reflexiveanti-symmetric, if "a is related to b and b is related to c" implies that a issymmetricNone from the choices

Answered: Ris said to be. reflexive symmetric…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Considering A as a set which contains the elements {2,3,4,5,6,7,8}, Define a relation R from A to A by R={(xy): y is multiple of x and x#y} [Multiple means "a number that may be divided by another a certain number of times without a remainder. Example: "15, 20, are multiples of 5" a. Write R b. Depict this relation R using an arrow diagram. c. Write the matrix representation for R. d. Check whether R is reflexive, symmetric, antisymmetric.
Given a set A = {1, 2, 3, 4}. Define a relation R on A as: R = {(x, y) | x - y is even} List the ordered pairs of the relation R. Is the relation R reflexive, symmetric, and transitive? Justify your answers.
Define relations R 1 , … , R 6 on { 1 , 2 , 3 , 4 } by R 1 = { ( 2 , 2 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 3 , 2 ) , ( 3 , 3 ) , ( 3 , 4 ) } , R 2 = { ( 1 , 1 ) , ( 1 , 2 ) , ( 2 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) , ( 4 , 4 ) } , R 3 = { ( 2 , 4 ) , ( 4 , 2 ) } , R 4 = { ( 1 , 2 ) , ( 2 , 3 ) , ( 3 , 4 ) } , R 5 = { ( 1 , 1 ) , ( 2 , 2 ) , ( 3 , 3 ) , ( 4 , 4 ) } , R 6 = { ( 1 , 3 ) , ( 1 , 4 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 3 , 1 ) , ( 3 , 4 ) } , Which of the following statements are correct? Check ALL correct answers below. A. R 2 is not transitive B. R 4 is antisymmetric C. R 5 is transitive D. R 6 is symmetric E. R 3 is transitive F. R 3 is reflexive G. R 3 is symmetric H. R 2 is reflexive I. R 4 is transitive J. R 5 is not reflexive K. R 4 is symmetric L. R 1 is not symmetric M. R 1 is reflexive
L. RELATIONS Let C= D= {-3, -2, -1, 1, 2, 3} and define a relation S from C to D as follows: For all (x, y)ECx D, (x, y) ER means that 1/x- 1/y is an integer. 1. a. Is 2 S 2? b. Is -1 S-1? c. Is (2, 2) E S? d. Is (2, -2) E S?
15 Part 2 of 4 Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Consider the following relations: R₁ = {(a, b) = R² | a> b), the greater than relation R₂ = {(a, b) ER² | a2 b), the greater than or equal to relation R3 = {(a, b) ER² | a< b), the less than relation R₁ = {(a, b) ER² | a ≤ b), the less than or equal to relation R₁ = {(a, b) = R² | a = b), the equal to relation R6 = {(a, b) ER² | a b), the unequal to relation For these relations on the set of real numbers, find R₁⁰ R₁. Multiple Choice O O R₁ O R4
PLEASE TYPE ONLY**** DO ALL THREE QUESTIONS E, F, G SEE IMAGE ATTACHMENT*** Exercise 8.1.4: Arrow diagrams for relations on small finite sets.Draw the arrow diagram for each relation. (e) The domain for the relation P is the set {2, 4, 8, 10, 16, 64}. For x, y in the domain, xPy if there is a positive integer n such that xn = y
17 Part 4 of 4 Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Consider the following relations: R₁ = {(a, b) € R² | a> b), the greater than relation R₂ = {(a, b) ER² | a2 b), the greater than or equal to relation R3 = {(a, b) ER² | a< b), the less than relation R₁ = {(a, b) ER² | a ≤ b), the less than or equal to relation R₁ = {(a, b) = R² | a = b), the equal to relation R₁ = {(a, b) € R² | a‡ b), the unequal to relation For these relations on the set of real numbers, find R₁ R6. Multiple Choice O O о R5 R² R6
Let A = {-1,0, 1} and R be a relation on A such that R = {(a,b)|a² = b}. Select all properties of this relation. reflexive symmetric anti-symmetric transitive equivalence relation partial order
14 Part 1 of 4 Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Consider the following relations: R₁ = {(a, b) = R² | a> b), the greater than relation R₂ = {(a, b) € R2 R3 = {(a, b) € R² | a < b), the less than relation R₁ = [(a, b) ER² | a ≤ b), the less than or equal to relation R5 = {(a, b) € R² | a= b), the equal to relation R₁ = {(a, b) = R² | a b), the unequal to relation For these relations on the set of real numbers, find R₂0 R2. Multiple Choice R4 R3 I az b), the greater than or equal to relation R2 R₁
Let A = {3, 4, 5} and B = {5, 6, 7}, and let S be the "divides" relation from A to B. That is, for every ordered pair (x, y) E Ax B, x Sy x|y. Which ordered pairs are in S and which are in S-? (Enter your answers in set-roster notation.) {1} S = %3D S-1
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