Let C be the circle relation defined on the set of real numbers. For every x, y Є R, x Cy ⇒ x² + y² = 1. (a) Is C reflexive? Justify your answer. C is reflexive for every real number x, x C x. By definition of C this means that for every real number x, = 1. This is ---Select--- ✓ . Find an example x and x² + x2 that show this is the case. (x, x² + x²) = Since this ---Select--- 1, C-Select--- reflexive. (b) Is C symmetric? Justify your answer. x² + C is symmetric >> for all real numbers x and y, if x C y then ? ✓ C ? V. By definition of C, this means that for all real numbers x and y, if x² + y² = y ² ? V ? ✓ + x² for ---Select--- ✓ real numbers x and y. Thus, C ---Select--- ✓ symmetric. then ? ✓ + x = . This is ---Select--- ✓ because, by the commutative property of addition, (c) Is C transitive? Justify your answer. C is transitive >> for all real numbers x, y, and z, if x C y and y C z then x C z. By definition of C this means that for all real numbers x, y, and z, if x² + y² following numbers entered as a comma-separated list. = 1 and y² + ? ✓ = 1 then x² + ? = 1. This is --Select--- ✓ . For example, let x, y, and z be the (x, y, z) = Then x2 + y²?V y²+ ? ✓ , and x² + ? V ? 1. Thus, C ---Select--- ✓ transitive.
Let C be the circle relation defined on the set of real numbers. For every x, y Є R, x Cy ⇒ x² + y² = 1. (a) Is C reflexive? Justify your answer. C is reflexive for every real number x, x C x. By definition of C this means that for every real number x, = 1. This is ---Select--- ✓ . Find an example x and x² + x2 that show this is the case. (x, x² + x²) = Since this ---Select--- 1, C-Select--- reflexive. (b) Is C symmetric? Justify your answer. x² + C is symmetric >> for all real numbers x and y, if x C y then ? ✓ C ? V. By definition of C, this means that for all real numbers x and y, if x² + y² = y ² ? V ? ✓ + x² for ---Select--- ✓ real numbers x and y. Thus, C ---Select--- ✓ symmetric. then ? ✓ + x = . This is ---Select--- ✓ because, by the commutative property of addition, (c) Is C transitive? Justify your answer. C is transitive >> for all real numbers x, y, and z, if x C y and y C z then x C z. By definition of C this means that for all real numbers x, y, and z, if x² + y² following numbers entered as a comma-separated list. = 1 and y² + ? ✓ = 1 then x² + ? = 1. This is --Select--- ✓ . For example, let x, y, and z be the (x, y, z) = Then x2 + y²?V y²+ ? ✓ , and x² + ? V ? 1. Thus, C ---Select--- ✓ transitive.
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...
Related questions
Question
need help
Transcribed Image Text:Let C be the circle relation defined on the set of real numbers.
For every x, y Є R, x Cy ⇒ x² + y² = 1.
(a) Is C reflexive? Justify your answer.
C is reflexive for every real number x, x C x. By definition of C this means that for every real number x,
= 1. This is ---Select--- ✓ . Find an example x and x² + x2 that show this is the case.
(x, x² + x²)
=
Since this ---Select---
1, C-Select--- reflexive.
(b) Is C symmetric? Justify your answer.
x²
+
C is symmetric >> for all real numbers x and y, if x C y then ? ✓ C ? V. By definition of C, this means that for all real numbers x and y, if x² + y² =
y ² ? V ? ✓ + x² for ---Select--- ✓ real numbers x and y. Thus, C ---Select--- ✓ symmetric.
then ? ✓ + x =
. This is ---Select--- ✓ because, by the commutative property of addition,
(c) Is C transitive? Justify your answer.
C is transitive >> for all real numbers x, y, and z, if x C y and y C z then x C z. By definition of C this means that for all real numbers x, y, and z, if x² + y²
following numbers entered as a comma-separated list.
= 1 and y²
+ ? ✓
= 1 then x² + ?
= 1. This is --Select--- ✓ . For example, let x, y, and z be the
(x, y, z) =
Then x2 + y²?V
y²+
? ✓
, and x² + ? V
? 1. Thus, C ---Select--- ✓ transitive.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning