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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7. Let P=[[a.b,d),[c.f).fe.g]] be a partition. Write the relation matrix for the implied equivalence relation.
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 A × B| (x, y) ERor (x, y) E S} RO S= {(x, y) E A x B | (x, y) ERand (x, y) E S}. Let A = {-4, 4, 7, 9} and B = {4, 7}, and define relations R and S from A to B as follows. For every (x, y) E Ax B, x R y x| = [y] and x Sy x - y is even. Which ordered pairs are in A x B, R, S, R U S, and RN S? (Use set-roster notation to enter your answers.) Ax B = R = S = RUS = ROS =
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 =
1. Let A = {1,2,3,4,5,6), and consider the following equivalence relation on A: R = {(1, 1), (2, 2), (3, 3), (4,4), (5,5), (6, 6), (2, 3), (3, 2), (4, 5), (5, 4), (4, 6), (6,4), (5,6), (6,5)} List the equivalence classes of R. 2. Let A = {a,bed el Suppose A is an equivalence relation on 4. Suppose R bes two equivaler.se alasses. Also wad, Re and aRd Write out R as a cot 3. Let A = {a,b,c,d,e}. Suppose R is an equivalence relation on A. Suppose R has three equivalence classes. Also aRd and bRc. Write out R as a set. 4. Let A {a,b,c,d,e). Suppose A is an equivalence relation on 4. Suppose also that anta and one, aRa and cite. How many equivalones classes dees At have! CIV 5. There are two different equivalence relations on the set A = {a,b}. Describe them. Diagrams will suffice.
1. Find the union C1 U C2 and the intersection C1n C2 of the two sets C1 and C2, where (a) C1 = {0, 1, 2, }, C2 = {2,3, 4}. (b) C1= {x:0 < x <2}, C2= {x :1
b. A particle moves in simple harmonic motion according to the equation, S = 09A cos(wt) + 09B cos(wt). Where s is the displacement, w is the angular d2 +ws=0. 'dt2 frequency and A, B are constant. Show that,
1 1 1 c) The matrix M = 1 ㅇ represents the relations R defined 1 1 L1 0 0 1. the set A = {1, 2, 3, 4}. i) List the ordered pairs in the relation R. i) Draw the graph representing the relation R. d) How many edges does a 50–regular graph with 100 vertices have?
Please do Exercise 17.1.13 part A,B,C,D and please show step by step and explain
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)