(5.) Consider the unit circle C with equation x + y = 1 in the plane. Thus C = {(x, y) ERX R: x + y = 1}. Define a relation ~ on C as follows: For (x, y) E C, (x, y) is related to itself and to its antipodal point (-x, -y). In symbols, (x, y)~ (x, y); (x, y) ~(-x, y). (a) Show that is an equivalence relation. (b) Think of C as a rubber band and imagine gluing together the equivalent antipodal points of C. Describe the resulting figure. (Much more will be said on this topic in Chapter 7.)