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 Cx. 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. C is symmetric >> for all real numbers x and y, if x Cy then ? VC? . By definition of C, this means that for all real numbers x and y, if x² + y² |---Select--- real numbers x and y. Thus, C ---Select--- ✓ symmetric. (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 separated list. (x, y, z) = Then x² + y²? y²+ and x²+? V ? 1. Thus, C ---Select--- ✓ transitive. then? V + x² = This is ---Select--- ✓ because, by the commutative property of addition, x² + y² ? v ? + x² for = 1 and y² + ? =1 then x² + ? V = 1. This is --Select--- ✓ For example, let x, y, and z be the following numbers entered as a comma-
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 Cx. 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. C is symmetric >> for all real numbers x and y, if x Cy then ? VC? . By definition of C, this means that for all real numbers x and y, if x² + y² |---Select--- real numbers x and y. Thus, C ---Select--- ✓ symmetric. (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 separated list. (x, y, z) = Then x² + y²? y²+ and x²+? V ? 1. Thus, C ---Select--- ✓ transitive. then? V + x² = This is ---Select--- ✓ because, by the commutative property of addition, x² + y² ? v ? + x² for = 1 and y² + ? =1 then x² + ? V = 1. This is --Select--- ✓ For example, let x, y, and z be the following numbers entered as a comma-
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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 Cx. 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.
C is symmetric >> for all real numbers x and y, if x Cy then ? VC? . By definition of C, this means that for all real numbers x and y, if x² + y²
|---Select--- real numbers x and y. Thus, C ---Select--- ✓ symmetric.
(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
separated list.
(x, y, z) =
Then x² + y²?
y²+
and x²+? V
? 1. Thus, C ---Select--- ✓ transitive.
then? V
+ x² =
This is ---Select--- ✓ because, by the commutative property of addition, x² + y² ? v
? + x² for
= 1 and y²
+ ?
=1 then x² + ? V
= 1. This is --Select--- ✓ For example, let x, y, and z be the following numbers entered as a comma-
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 1 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
