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Let C be the circle relation defined on the set of real numbers. For every x, y ER, XCyx² + 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, show this is the case. (x, x² + x²) = Since this does not equal✔ 1, C is not (b) Is C symmetric? Justify your answer. C is symmetric for all real numbers x and y, if x C y theny y² + x² = | This is true ✓ ✔ IS ✔ symmetric. (c) Is C transitive? C is transitive x² +2²✔✔ (x, y, z) = reflexive. Then x² + y²✔ ], y² +2²=✔ X = 1. This is false and x² + 2✔✔✔✔ 1. Thus, C is not ✓ ✓ CX✔✔ By definition of C, this means that for all real numbers x and y, if x² + y2 = | because, by the commutative property of addition, x2 + y² =✔✔✔✔✔ + x² for all Justify your answer. 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 = 1 and y2 + 2✔✔✔ = 1 then = 1. This is false . For example, let x, y, and z be the following numbers entered as a comma-separated list. ✓ ✓ Find an example x and x2 + x2 that ✔✔✔ transitive. then real numbers x and y. Thus, C ►

Let C be the circle relation defined on the set of real numbers. For every x, y ER, XCyx² + 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, show this is the case. (x, x² + x²) = Since this does not equal✔ 1, C is not (b) Is C symmetric? Justify your answer. C is symmetric for all real numbers x and y, if x C y theny y² + x² = | This is true ✓ ✔ IS ✔ symmetric. (c) Is C transitive? C is transitive x² +2²✔✔ (x, y, z) = reflexive. Then x² + y²✔ ], y² +2²=✔ X = 1. This is false and x² + 2✔✔✔✔ 1. Thus, C is not ✓ ✓ CX✔✔ By definition of C, this means that for all real numbers x and y, if x² + y2 = | because, by the commutative property of addition, x2 + y² =✔✔✔✔✔ + x² for all Justify your answer. 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 = 1 and y2 + 2✔✔✔ = 1 then = 1. This is false . For example, let x, y, and z be the following numbers entered as a comma-separated list. ✓ ✓ Find an example x and x2 + x2 that ✔✔✔ transitive. then real numbers x and y. Thus, C ►

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Let C be the circle relation defined on the set of real numbers. For every x, y ER, x Cyx² + 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, show this is the case. (x, x² + x²) = = Since this does not equal ✔1, C is not y² v IS (b) Is C symmetric? Justify your answer. C is symmetric for all real numbers x and y, if x C y theny This is true x² (c) Is C transitive? C is transitive x²2+z²v (x, y, z) = T symmetric. V = ✔ reflexive. Then x2 + y2✓ ✓ X Cxv✔ By definition of C, this means that for all real numbers x and y, if x² + y² y2 because, by the commutative property of addition, x2 + y² = √² + x2 for all , y² + z² =✔, and x² + 22² V 1. Thus, C is not = 1. This is false را Justify your answer. for all real numbers x, y, and z, if x C y and y Cz then x C z. By definition of C this means that for all real numbers x, y, and z, if x² + y² = 1 and y² + 2² v 1. This is false For example, let x, y, and z be the following numbers entered as a comma-separated list. = transitive. Find an example x and x² + x2 that then real numbers x and y. Thus, C 27 = 1 then
Transcribed Image Text:Let C be the circle relation defined on the set of real numbers. For every x, y ER, x Cyx² + 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, show this is the case. (x, x² + x²) = = Since this does not equal ✔1, C is not y² v IS (b) Is C symmetric? Justify your answer. C is symmetric for all real numbers x and y, if x C y theny This is true x² (c) Is C transitive? C is transitive x²2+z²v (x, y, z) = T symmetric. V = ✔ reflexive. Then x2 + y2✓ ✓ X Cxv✔ By definition of C, this means that for all real numbers x and y, if x² + y² y2 because, by the commutative property of addition, x2 + y² = √² + x2 for all , y² + z² =✔, and x² + 22² V 1. Thus, C is not = 1. This is false را Justify your answer. for all real numbers x, y, and z, if x C y and y Cz then x C z. By definition of C this means that for all real numbers x, y, and z, if x² + y² = 1 and y² + 2² v 1. This is false For example, let x, y, and z be the following numbers entered as a comma-separated list. = transitive. Find an example x and x² + x2 that then real numbers x and y. Thus, C 27 = 1 then
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