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 Cx. By definition of C this means that for every real number x, x² + x² (x, x² + x²) = (x,1 × Since this does not equal 1, C is not reflexive. 1. This is false . Find an example x and x² + x2 that show this is the case. then +x=1 This is true because, by the commutative property of addition, (b) Is C symmetric? Justify your answer. C is symmetric for all real numbers x and y, if x Cy then y✔Cx ✓. By definition of C, this means that for all real numbers x and y, if x² + y² = 1 x²+y²=V74+x² for all real numbers x and y. Thus, C is (c) Is C transitive? Justify your answer. symmetric. C is transitive for all real numbers x, y, and z, if x Cy and y Cz then x Cz. By definition of C this means that for all real numbers x, y, and z, if x² + y2-1 and y²+ ZV entered as a comma-separated list. (x, y, z) (1,0), (0,1), (-1,0) Then x2+y2 V × ) y²+z² = and x²+2 1. Thus, C is not transitive. 1 then x²+V ♥1. This is false . For example, let x, y, and z be the following numbers