I need to find what is wrong with this proof and fix it. I know it's incorrect but I don't know how to fix it. (c) Give a geometric description of the set C.16. Evaluation of proofsSee the instructions for Exercise (19) on page 100 from Section 3.1.(a) Proposition. Let R be a relation on a set 4. If R is symmetric andtransitive, then R is reflexive.Proof. Let x V€A. If xR y, then y R xr since R is symmetric. Now,xRy and v R x, and since R is transitive, we can conclude that x Rx.Therefore, R is reflexive.

We use definition for following question

See the instructions for Exercise (19) on page T00 from Section 3,1 (a) Proposition. Let R be a relation on a set 4. If Ris symmetric and transitive, then R is reflexive Proof. Let x V€ A. If xR y, then v R xr since R is symmetric. Now, x Ry and v R x. and since R is transitive, we can conclude that x Rx. Therefore, R is reflexive.

See the instructions for Exercise (19) on page T00 from Section 3,1 (a) Proposition. Let R be a relation on a set 4. If Ris symmetric and transitive, then R is reflexive Proof. Let x V€ A. If xR y, then v R xr since R is symmetric. Now, x Ry and v R x. and since R is transitive, we can conclude that x Rx. Therefore, R is reflexive.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 14E: In each of the following parts, a relation is defined on the set of all human beings. Determine...

See similar textbooks

Similar questions

Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not reflexive.
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.
In Exercises , prove the statements concerning the relation on the set of all integers. 18. If and , then .
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.
13. Consider the set of all nonempty subsets of . Determine whether the given relation on is reflexive, symmetric or transitive. Justify your answers. a. if and only if is subset of . b. if and only if is a proper subset of . c. if and only if and have the same number of elements.