Answered: 14. How many different relexive,…

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Advanced Math

14. How many different relexive, symmetric relations are there on the set {a,b,c}? O 10 none of these 8

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. (Relations) Consider the set A= {1,2, 3, 4, 5}, and a relation R defined by x Ry x2 – y is an integer multiple of 3. (a) List all elements y for which 1Ry is true. (b) Is R reflexive? Justify. (c) Is R symmetric? Justify. (d) Is R antisymmetric? Justify. (e) Is R transitive? Justify.
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1. We are given the sets S and V: S = {Anne, Theo} V {studies, runs, meditates} = (a) Find the Cartesian Product of S and V: S x V (b) A relation R. is a subset of the Cartesian product. Create such a subset RC (S X V) with three elements.
6. Q6; Relations (a) Define relations S and R on the set A = {a, b, c, d} as follows: {(a, b), (b, c), (c, d), (b, b)}, S = R = {(b, a), (c, c), (a, c), (d, b)}. i. Find So S, So R, R-o So R. Is R-lo SoR= S ? ii. Determine which of S, R, So R, S-1 or R-1 is a function. (b) Let R = {(x, y) E R × R : 1
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 =
15. Let C = {(2n + 1)³:n € R } and D = {2n + 1:n € R}. What is the relation between these two sets? State and prove your answer.
part b and c
Enter an example of an equivalence relation R on the set X = {0, 1, 5, 6, 8} such that all of the following are true: ● • (5,0) = R; (8, 6) # R; |[1] R = 2. ●
A={1,2,3,4,5,6} and consider the following 3 subsets of A. A = {1,3,5}; A2 = Let {2, 4, 6}; A3 = {3, 6}.
Question Number 06 a) For the relation R on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is an equivalence relation. R = {(1,3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)} b) Determine whether the graph is bipartite. od c) Draw these graphs i) W; ii) K4