Just number 5 please 4. Show that congruence modulo n is an equivale 5. Consider the...

4. Show that congruence modulo n is an equivale 5. Consider the unit circle C with equation modulo n is an equivalence relation UI arcle C with equation x2 + y2 = 1 in the plane. Thus C = {(x, y) ERX R: x2 + y2 = 1}. Define a relation on C as follows: For (x, y) EC, antipodal point (-x, -y). In symbols, llows: For (x, y) E C (x, y) is related to itself and to its allo (x, y) ~ (x, y); (x, y) ~ (-x, -y). (a) Show that is an equivalence relation. 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.)

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