QUESTION 12Let R={ (a,a), (a,b). (b,b). (b,a). (CC). (d,d), (e,e), (f,f). (d,e), (e,d). (e,f), (f.e), (d,f). (1,d)} be an equivalence relation on the set A.a. List the elements in the set Ab. List the sets in the partition of the set A defined by the equivalence :elation R using correct set notationDo not upload your solution here, but wait until you have left the Lockdown browser and use the link in Week 6Attach FileJorganPonteat Collection

Given: R = (a, a), (a, b), (b, b), (b, a), (c, c), (d, d), (e, e), (f, f), (d, e), (e, d), (e, f),…

Let R={ (a,a). (a,b). (b.b). (b,a). (CC). (d,d), (e,e), (f,f). (d,e), (e,d). (e,f), (f.e). (d.f). (f.d)) be an equivalence relation on the set A. a. List the elements in the set A b. List the sets in the partition of the set A defined by the equivalence relation R using correct set notation

Let R={ (a,a). (a,b). (b.b). (b,a). (CC). (d,d), (e,e), (f,f). (d,e), (e,d). (e,f), (f.e). (d.f). (f.d)) be an equivalence relation on the set A. a. List the elements in the set A b. List the sets in the partition of the set A defined by the equivalence relation R using correct set notation

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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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 reflexive and symmetric but not transitive. O b. Ris reflexive and transitive but not symmetric. O c. Ris reflexive, symmetric and transitive. O d. Ris symmetric and transitive but not reflexive. R is not reflexive neither symmetric but it is transitive. O e.
For the set A = {are, bot, cab, era}, define the relation R on A to be: (x,y) e R if and only if word x and word y share one letter only. For example (are, cab) is in R because those words share one letter only ("a"). But (are, era) is NOT in R because those words do NOT share one letter only, they share 3 letters. Also (bot, era) is NOT in R since they share no letters at all. In cach part, answer yes or no. If yes, then explain why in terms of this specific relation about sharing letters (not just by stating the generic definition of the property). If you say a) Is R reflexive? b) Is R symmetric? c) Is R antisymmetric? d) Is R transitive?
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25, 26, 27
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
. 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) }
Let R be an equivalence relation on A = {0, 7, 8, 9} and R = {(7, 8), (8,9), (9, 9), (7, 7), (8, 8), (7, 9), (9, 7), (9, 8), (8, 7), (0, 0)}. Answer each of the following questions. [8] = [7] = [9] = [0] =
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.
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).
Let S = {a, b, c}. Then R = {(a, b)} is a relation on S. Which of the properties reflexive, symmetric andtransitive does the relation R possess? I know that its not reflexive or symmetric but its vacuously transitive, but I dont get why, so please explain step by step
Give examples of relations R and S on Z such that (a) Both R and S are not equivalence relations but R+ S is. (b) Both R and S are not partial order relations but R+ S is. Show that if both R and S are equivalences relations, then R+S is not an equivalence relation.