Please explain each property (withs #'s) Recall that for x, y ≤ R, |x - y ≤ R is the absolute value of x-y. That is, (x-y -(x-y) Define the binary relation R on R as follows: Is this binary relation reflexive symmetric antisymmetric transitive |x - y = if x-y 20 ifx-y<0. xRy if x - y < 1. For each of these properties provide a justification why it is satisfied or a counterexample why not.

Please explain each property (withs #'s) Recall that for x, y ≤ R, |x - y ≤ R is the absolute value of x-y. That is, (x-y -(x-y) Define the binary relation R on R as follows: Is this binary relation reflexive symmetric antisymmetric transitive |x - y = if x-y 20 ifx-y<0. xRy if x - y < 1. For each of these properties provide a justification why it is satisfied or a counterexample why not.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter1: Line And Angle Relationships

Section1.4: Relationships: Perpendicular Lines

Problem 17E: Does the relation is a brother of have a reflexive property consider one male? A symmetric property...

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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.
Does the relation is a brother of have a reflexive property consider one male? A symmetric property consider two males? A transitive property consider three males?
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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.