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

Just number 5 please
4. Show that congruence modulo n is an equivale 5. Consider the unit circle C with equation modulo n is an equivalence relati
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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2.5 the consider the Unit Circle x² + y2 ad in Plane. c=1 (L, DEIRXIR : x2 + y2 , ? Define a Relation n on c. asa (36,9)n (,y(021,9,) = (22,427 OR (-2,-40) = (12,42) & 4 = 42 sa=X2 OR -21-22 2 -4,-92 (22,42) = (1,9,) OR (-30, ,-4,) (X2,92) - (24,I)By eq O and ☺ 24 = 72 OR 3,5-tz And % = %3 OR %=-63 We can conclude that Oye Hyor. 83 5 Similarly By eq o and we can conclud(B) Think of c as a rubber Band and Imagine gleing together the equircalent antipodal Point of c. Describle the for resulting

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