Exercise 2.10. A poset (or partially ordered set) is a relation R which is reflexive, transitive, and antisymmetric: (i.e., (x, y) E R and (y, x) ER implies r =y). Prove that the following are posets: !! (i) R= {(A, B) E 2ª × 2R : A C B} (ii) R= {(x,y) ER × R: r < y}

Exercise 2.10. A poset (or partially ordered set) is a relation R which is reflexive, transitive, and antisymmetric: (i.e., (x, y) E R and (y, x) ER implies r =y). Prove that the following are posets: !! (i) R= {(A, B) E 2ª × 2R : A C B} (ii) R= {(x,y) ER × R: r < y}

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Q6; Relations (a) Define relations S and R as follows: S = {(a,b), (b, c), (c, d), (b, b)}, R = {(b,…

A: Solution is in next step

Q: b) Let A = {0, 1, 3,4, 5, 6} and define the relation R and S on A as follows: For every (x, y) €A,…

A: all the ordered pairs (x,y) in the relation R and S and SoR are given below...

Q: How many elements are in the Cartesian product U x V? * Let U = {u is odd | 9 < u < 14} and V = {v €…

Q: In Q1-Q4 prove why each relation has or does not have the properties: reflexive, symmetric,…

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}. Choosethe correct…

A: Given : Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}. Choosethe…

Q: a)Let R be a relation on the set Z × Z defined by the following rule: For all (a, b),(c, d) ∈ Z × Z,…

Q: 6.A. Let A = (1, 2, 3) and B = (1, 2, 3, 4) and define a relation R from A to B as Given any (x. y)…

Q: A). C). X y y 7 - 2 - 2 - 1 - 1 - 4 4 - 5 1 1 -4 1 - 2 - 5 1 y 1 y B). D). - 2 - 2 - 1 6. 8. - 1 0.…

Q: Disprove that for any relations R and S, ran(S • R) = ran(S).

Q: 2. Let R = {(x, y) = R x R = |x] + [y] =4}. Then R is a relation on R. Is R an equivalence relation…

Q: 2. For universe S = R² define relation as: (a, b) ≤ (c,d) ⇒ 2a-b≤2c-d. For each of the properties…

A: Definitions: Consider a relation R on a set S satisfying the following properties:R is reflexive,…

Q: 2) Define a relation R from {a, b, c} to {u, v} as follows: R = {(a, v),(b, u),(b, v),(c, u)}. a)…

Q: (a) Consider the set A = {x² E Q1x ER}. Determine whether A is closed under addition and…

Q: 10) Let R be a relation on A = {1,2,3,4,5,6,7} as x R yx + y = 6. a. Find relative set R(B), where B…

A: (10) Consider the provide question, (a)

Q: 1. Suppose A = {a, b, c, d}. Judge the following relations on A with respect to reflexive,…

A: Since this is the multiple question type, according to the Bartleby Answering rule, only first…

Q: () -- () --()-() --- Let vi = 2 v2 = 4. 5, v3 = 6 v4 = 6. 7 If is a depen- 1 dence relation on (v1,…

Q: 1. Define a relation R on R? by stating that (a, b)R(c, d) if and only if a? + b <c? +d². Show that…

Q: 1. Let R be the relation on N defined by "aRb if EN or 5| (b- a)". So for example (6, 2) € R and…

Q: 1), consider the relation of R= {(0, 0), (1, 1), (1, 3), (2, 2), (2, 3), (3, 1), (3, 2),(3, 3)…

Q: b) The relation R on A = {a, b, c, d} is defined by the following digraph. b (i) List all paths of…

A: (i) Paths of length 2 are a-b-d, c-d-c, a-c-d, d-d-c, c-c-d, d-d-a

Q: Let fi = 1+a +x², f2 = 3 + 2x +x², f3 = 1+2x + 3x², fa = 1+3r + 5æ². If is a dependence relation on…

A: We have to solve given problem:

Q: f d a h с 6.0 g e b

Q: (Relations) Consider the set A = {1,2, 3, 4, 5}, and a relation R defined by x Ry + x² – y is an…

A: Since you have posted a multipart question and we can answer three subparts. So, answered the first…

Q: Let R be a relation from A to B and S a relation from B to A. Prove or disprove that if S of R =…

Q: Let R = {(0, 0), (1, 1), (-1, -1)} be a relation on set A. Deduce the rule between x and y for order…

Q: Let R = {(1, 1),(1, 2),(2, 1),(2, 2),(3, 3)}. be a relation on a set A= 1,2,3}, the R is %3D…

A: Given R={(1,1),(1,2),(2,1),(2,2),(3,3)} relation on set A={1,2,3} Anti-symmetric: A Relation R of a…

Question

Exercise 2.10. A poset (or partially ordered set) is a relation R which is reflexive, transitive,
and antisymmetric: (i.e., (x, y) E R and (y, x) e R implies r = y). Prove that the following
are posets:
(i) R= {(A, B) € 2ª × 2R : A C B}
(ii) R= {(x,y) E R × R : r < y}

Posets:
Exercise 2.11. Prove that n
+.
for all n E Z.
2

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Relations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

. 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 a relation from A to B and S a relation from B to A. Prove or disprove that if S of R = IdA, then S is surjective. If the assertion is not true, find additional assertions that will make it true.
2. Let A := {1,2,3,4}: B and T:= {(a, b) E A x B | +¹ € Z}. (a) Find A x B. (b) Find T. (c) Check what property of Relations thus T have. Provide a brief explana- tion for each property.
Let be the relation on True False N defined by R={(n, m) : m³ = n + 1). Then R is one-to-one.
17. Let R and S be relations on A= {1, 2, 3, 4} defined by R={(a, b) :b=5-a} and S = {(a, b): a
(b) Let R = {(1, 1), (1, 2),(2, 1), (2, 2),(3, 3)}. be a relation on a set A = {1,2,3} , the R is Antisymmetric and transitive. ii. i. Not antisymmetric, and not transitive Antisymmetric, and not transitive iv. iii. Non of these
11. Let C= {O, 1, 2) and D = (2, 4, 6, 8) and define a relation R from A to B as follows: For all (x, y) E AXB, %3D %3D y+2 (x, y) e R means that is an integer. a. Is 1 R 2? Is 2 R 8? Is (1, 8) e R? Is (2, 6) e R ? b. Write R as a set of ordered pairs. c. Write the domain and co-domain of R. d. Draw an arrow diagram for R.