[Each of the operations below is a relation on N x N where 0 E N. Tell which relations has which property by writing true or false into each empty cell of the table below. No explanation is needed. Symmetric Reflexive Transitive Equivilence Relation less than greater than or equal to Absolute Value Function

[Each of the operations below is a relation on N x N where 0 E N. Tell which relations has which property by writing true or false into each empty cell of the table below. No explanation is needed. Symmetric Reflexive Transitive Equivilence Relation less than greater than or equal to Absolute Value Function

Name: I need help solving this please! [Each of the operations below is a re
Uploaded: 2024-03-20T07:06:27.000Z
Channel: Bartleby
Description: I need help solving this please! [Each of the operations below is a relationon N x N where 0 E N. Tell which relations has which property by writing true or false into eachempty cell of the table below. No explanation is needed.Symmetric ReflexiveTra

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 17E: In each of the following parts, a relation R is defined on the power set (A) of the nonempty set A....

See similar textbooks

Similar questions

In each of the following parts, a relation R is defined on the power set (A) of the nonempty set A. Determine in each case whether R is reflexive, symmetric, or transitive. Justify your answers. a. xRy if and only if xy. b. xRy if and only if xy.
(See exercise 24.) Show that the relation f(x)Rg(x) if and only if f(x)=g(x) is an equivalence relation on R[ x ]. Describe the equivalence class [ f(x) ]. For each f(x)=i=0naixi in R[ x ], the formal derivative of f(x) is the polynomial f(x)=i=1niaixi1. (For n=0, f(x)=0 by definition.) Prove that [ f(x)+g(x) ]=f(x)+g(x). Prove that [ f(x)g(x) ]=f(x)g(x)+f(x)g(x).
2. In each of the following parts, a relation is defined on the set of all integers. Determine in each case whether or not is reflexive, symmetric or transitive. Justify your answers. a. if and only if . b. if and only if . c. if and only if for some in . d. if and only if . e. if and only if . f. if and only if . g. if and only if . h. if and only if . i. if and only if . j. if and only if . k. if and only if .
Label each of the following statements as either true or false. Let R be a relation on a nonempty set A that is symmetric and transitive. Since R is symmetric xRy implies yRx. Since R is transitive xRy and yRx implies xRx. Hence R is alsoreflexive and thus an equivalence relation on A.
In each of the following parts, a relation is defined on the set of all human beings. Determine whether the relation is reflective, symmetric, or transitive. Justify your answers. xRy if and only if x lives within 400 miles of y. xRy if and only if x is the father of y. xRy if and only if x is a first cousin of y. xRy if and only if x and y were born in the same year. xRy if and only if x and y have the same mother. xRy if and only if x and y have the same hair colour.
A relation R on a nonempty set A is called asymmetric if, for x and y in A, xRy implies yRx. Which of the relations in Exercise 2 areasymmetric? In each of the following parts, a relation R is defined on the set of all integers. Determine in each case whether or not R is reflexive, symmetric, or transitive. Justify your answers. a. xRy if and only if x=2y. b. xRy if and only if x=y. c. xRy if and only if y=xk for some k in . d. xRy if and only if xy. e. xRy if and only if xy. f. xRy if and only if x=|y|. g. xRy if and only if |x||y+1|. h. xRy if and only if xy i. xRy if and only if xy j. xRy if and only if |xy|=1. k. xRy if and only if |xy|1.