1. For each of the following binary relations p on Z, decide which of the given ordered pairs belong toP.(a) xpy xly; (2, 6), (3, 5), (8, 4), (4,8)(b) xpy →x and y are relatively prime; (8,5), (9, 16), (6, 8), (8, 21)(c) xpy GCD(x, y) = 7 (28, 14), (7, 7), (10, 5), (21, 14)

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Answered: 1. For each of the following binary…

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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This question refers to unions and intersections of relations. Since relations are subsets of Cartesian products, their unions and intersections can be calculated as for any subsets. Given two relations R and S from a set A to a set B, RUS = {(x, y) E AXB I (x, y) ER or (x, y) E S} RNS = {(x, y)E AXB| (x, y) ER and (x, y) Es}. Let A = {-2, 2, 3, 5} and B = {2, 3} and define relations R and S from A to B as follows: For every (x, y) E Ax B, x R y - |x| = lyl and xsyex - y is even. Using set-roster notation, state explicitly which ordered pairs are in A x B, R, S, RU S, and RN s. (Enter your answers as comma-separated lists of ordered pairs.) AXB = R = S = RUS = ROS =
2. Given a relation, R on A = {a, b, c, d} on as follows: R = {(a, a), (a, b), (a, d), (b, b), (b, c), (c, c), (c, d), (d, a), (d, d)} %3D Show the matrix of relation, MR and determine whether the relation, R is an equivalence relation.
Consider z and the binary relation on A given by R=( (x.y)lx+y = 10) For each item, fill the blank by using Y if the binary relation satisfies the property and N if the binary relation does not satisfy the property 1.( ) Reflexive 2( ) Symmetric 3. ( )Antisymmotric 4. ( ) Transitive
4. Let A := {1, 2, 3, 4} := B. (a) What is the cartesian product of A and B. (b) Find S := {(a, b)|f € Z}. (d) Is S a Partial Order? Justify your answer.
Explain whny the following binary relation on. 1,2,3} Is not R= {(1,1)(1,2),(1,3),(2,1).(2,2).(3,3)}|
Please do Exercise 17.1.13 part A,B,C,D and please show step by step and explain
6) Let A = {4,5,6} and B = {3,6,7}. Define relations U, V, and W from A to B as follows, For all (x, y) E A×B, (x, y) eU x>y (x, y) e V > X-y is an integer. W = {(4,7), (6,3), (5,6)} Indicate whether any of the relations U, V, and W are functions from A to B.
discrete math

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1. For each of the following binary relations p on Z, decide which of the given ordered pairs belong to P. (a) xpy xly; (2, 6), (3, 5), (8, 4), (4,8) (b) xpy →x and y are relatively prime; (8,5), (9, 16), (6, 8), (8, 21) (c) xpy GCD(x, y) = 7 (28, 14), (7, 7), (10, 5), (21, 14)