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.