Let R be the relation on R defined byR= {(x, y) E R × R | x² + y²4 or x = y}.Answer each of the following parts by givingeither a proof or a counterexample.Is R a function from R to R?Is R antisymmetric? Is R symmetric?Determine whether for x, y E R the statementVx 3y (xRy) is true or false.Determine whether for x, y E R the statement3y Va (xRy) is true or false.

Given that R be the relation on ℝ defined by,R=x,y∈ℝ×ℝx2+y2=4 or x=y2

Answered: Let R be the relation on R defined by…

Let R be the relation on R defined by R= {(x, y) E R × R | x² + y² = 4 or x = y²}. Answer each of the following parts by giving either a proof or a counterexample.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 24E: For any relation on the nonempty set, the inverse of is the relation defined by if and only if ....

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Question

Let R be the relation on R defined by
R= {(x, y) E R × R | x² + y²
4 or x = y}.
Answer each of the following parts by giving
either a proof or a counterexample.
Is R a function from R to R?
Is R antisymmetric? Is R symmetric?
Determine whether for x, y E R the statement
Vx 3y (xRy) is true or false.
Determine whether for x, y E R the statement
3y Va (xRy) is true or false.

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