Relations Discrete Mathematics

Question

Question

For each of the following relations on the set Z, determine if it is a partial order. (a) {(a, b): a^2 – b^2 = b^2 – a^2} (b) {(a, b): a^2 – b^2 ≤ 1}

Answer 1

Similar Homework Help Questions

Determine whether each of the relations defined below on the set of positive integers is a...

Determine whether each of the relations defined below on the set of positive integers is a partial order? (a) (x,y) ϵ R if x ≥ y (b) (x,y) ϵ R if 3 divides x+y
Python 3 Discrete Mathematics We are going to write a program to read in relations, show...

Python 3 Discrete Mathematics We are going to write a program to read in relations, show the matrix of the relation. We will also show if the relation is reflexive, symmetric, anti-symmetric and transitive. This program will read in files that the user gives. Normal Error handling applies. The file the user gives you will have the elements of the set for the relation followed by the tuples in the relation. The Text Files The first line of the text...
discrete mathematics help 1. List the order pairs in the relation R from A ={0, 1,...

discrete mathematics help 1. List the order pairs in the relation R from A ={0, 1, 2, 3, 4} to B = {0, 1, 2, 3}, where (a, b) Î R if and only if a) a = b b) a + b = 4 c) a > b d) a|b //6th edition ((a), (b), (c), and (d) of Exercise 1, Page 527.) 2. a) List all the ordered pairs in the relation R = {(a, b) |a divides b}...

Problem 3. Which of the following relations are equivalence relations on the given set S (1)...

Problem 3. Which of the following relations are equivalence relations on the given set S (1) S-R and ab5 2a +3b. (2) S-Z and abab 0 (4) S-N and a~b ab is a square. (5) S = R × R and (a, b) ~ (x, y)-a2 + b-z? + y2.
discrete maths 2. (Lewis, Zar 14.7) Determine whether each of the following relations is transitive, symmetric,...

discrete maths 2. (Lewis, Zar 14.7) Determine whether each of the following relations is transitive, symmetric, and reflexive and why: (a) The subset relation (b) The proper subset relation (c) The relation R on Z, where R(a, b) if and only if b is a multiple of a (d) The relation R on ordered pairs of integers, where R(<a,b>,<c,d >) if and only if ad-bc.
Topic: Discrete Mathematics and its Applications" Chapter 9:Equivalence Relations and Partial Orderings. 9. hash function H...

Topic: Discrete Mathematics and its Applications" Chapter 9:Equivalence Relations and Partial Orderings. 9. hash function H : {0,1)" → {0,1)" maps a bit string of length n to a bit string of length k. Hash functions are used to give a short label to a long string. The set of all "collisions" with a given string s defines an equivalence class for a given hash function H, that is: (a) What is the average cardinality of the equivalence classes [s]H...

10. For each of the following relations on the set of all real numbers, determine whether...

10. For each of the following relations on the set of all real numbers, determine whether it is reflexive, symmetric, antisymmetric, transitive. Here rRy if and only if: (b)-2y (d) ry -0 (f) x-1 or y 1 (h) ry-1 (a) x+ 2y-0 ( C)-y is a rational number (e) xy20 (g) z is a multiple of y
(1) Suppose R and S are reflexive relations on a set A. Prove or disprove each...

(1) Suppose R and S are reflexive relations on a set A. Prove or disprove each of these statements. (a) RUS is reflexive. (b) Rn S is reflexive. (c) R\S is reflexive. (2) Define the equivalence relation on the set Z where a ~b if and only if a? = 62. (a) List the element(s) of 7. (b) List the element(s) of -1. (c) Describe the set of all equivalence classes.
2. Consider the set A = {1, 2, 3, ... , 12} and the relations Em...

2. Consider the set A = {1, 2, 3, ... , 12} and the relations Em on A where x =m y means m divides x – y. (These are equivalence relations on A for the same reason as the similarly-defined relations on all of Z.) For each x E A, find the equivalence classes [x]=ş and [x]=4. Which =3 -equivalence classes are the same? Which 34 -equivalence classes are the same?

Given the following binary relations: The relation Rl on {w, 1, y, z), where R1 =...

Given the following binary relations: The relation Rl on {w, 1, y, z), where R1 = {(w, w), (w, 1), (x, w), (x, 1 ), (x, z), (y, y), (z,y),(2, 2)). The relation R2 on (a, b, c), where R2 = {(a, a ), (b, b), (c, c), (a, b), (a, c), (c, b)}. The relation R3 on {x,y,z}, where R3 = {(1, 2), (9,2), (2, y)}. Determine whether these relations are: (1) reflexive, (2) symmetric, (3) antisymmetric, (4) transitive?