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-