Let R be the equivalence relation on the set A = { a, b, c, d } induced by the partition ({a}; {b,c}; {d}). Select all pairs of elements in R.(a,a)(a,b)(a,c)O (a,d)(b,a)(b,b)(b,c)(b.d)(c.a)O (c,b)(c.c)(c,d)(d,a)O (d,b)(d,c)(d,d)

Given A = {a, b, c, d} partition {{a};{b, c};{d}}

Answered: Let R be the equivalence relation on…

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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Let A = {a, b, c, d} and let R = {(a, a), (a, b), (a, c), (a, d), (b, b), (b, c), (b, d), (c, c), (c, d), (d, d)} be arelation on A. Which of the properties reflexive, symmetric and transitive does the relation R possess? If Rdoes not possess one of these properties, explain why. How do I know where to stop? How do I know when I have proven transitivity? for example? I have difficulties with knowing if my prove is complete or not
. 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) }
2. Let A = {1,2, 3}, B = {4, 5, 6}, C = {7,8, 9}. Consider the relations R from A to B, S from B to C, and T on A. R = {(1, 5), (2, 4), (1, 6)} S = {(4, 8), (5, 7), (6, 8), (6, 9)} Т 3 {(1,2), (2, 3), (3, 1), (1, 1), (2, 2), (3, 3)} Find the following relations (a) Find the compositions Ro S, T o R, T o T. (b) Find the matrices MR, Ms, MT, MTOT, MTOR and MRos of the respective relations R, S, т, То Т, То R, and Ro S.
Let U be a universal set with subsets A and B such that n(U)=117, n(A)=60, n(B′)=68, n(A∩B)=15, n(B)=49, and n(A∪B)=94. Find the following: n((A∩B)′)=
A car dealership sells cars that were made in 2015 through 2020. Let the cars for sale be the domain of a relation R where 2 cars are related if they were made in the same year. b) Describe the partition defined by the equivalence classes. How do I do this?
The difference of two sets, A – B, is defined as the set containing all elements of A except those in B. That is, A - B = AN B'. Find A - B for the pair of sets if U = {1, 2, 3, 4, 5, 6, 7, 8, 9}. (Enter your answer in roster notation. Enter EMPTY or Ø for the empty set.) A = {3, 5, 9} and B = {2, 4, 6, 7, 8, 9} A - B =
11. For sets A and B, define AAB = (A \ B) U (B \ A). (a) Let A and B be sets. Prove that A = B if and only if AAB = 0. (b) Let A and B be sets. Prove that AAB = BAA. (c) Let A, B, and C be sets. Prove that (AAB) AC = AA (BAC).
2. Let U = {1, 2, 3} and A = U × U. In each case, show that = is an equivalence on A and find the quotient set A. (a) (a, b) = (a₁, b₁) if a + b = a₁ + b₁. (b) (a,b) = (a₁, b₁) if ab = a₁b₁. (c) (a, b) = (a₁, b₁) if a = a₁. (d) (a, b) = (a₁, b₁) if a - b = a₁-b₁.
List all the ordered pairs in the relation R = {(a, b)| gcd(a,b) = 1} on the set {2, 3, 4, 5, 6}.

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Let R be the equivalence relation on the set A = { a, b, c, d } induced by the partition ({a}; {b, c}; {d}). Select all pairs of elements in R. (a,a) (a,b) (a,c) (a,d) (b.a) (b.b) ☐ (b,c) (b,d) (c.a) ☐ (c,b) (c.c) ☐ (c,d) (d,a) (d,b) (d,c) (d,d)