25. Let R; = {x ER|Isx= 1 +}} = [1, 1+ }] for each positive integer i. 4 a. Ri = ? b. Ri = ? i=0 i=0 c. Are RI, R2, R3, . . . mutually disjoint? Explain. n n d. URi = ? e. Ri = ? i=0 i=0 00 00 f. URi = ? g. Ri = ? i= 0 i= 0 26. Let S; = xER| 1 2. Show that an = 3 .77-1 for every integer n 2 1. 25. A sequence bo, b1, b2, ... is defined by letting bo = 5 and bk = 4 + bk- for each integer k 2 1. Show that bn > 4n for every integer n 2 0.6. Let A = {x E Z x = 5a + 2 for some integer a), B = (yEZ y = 10b -3 for some integer b}, and C= {zEZ z = 10c +7 for some integer c). Prove or disprove each of the following statements. a. ACB b. BCA Hc. B = C 7. Let A = (x EZ x = 6a + 4 for some integer a), B = (yEZ y = 18b -2 for some integer b}, and C = {zEZ z = 18c + 16 for some integer c). Prove or disprove each of the following statements. a. ACB b. BCA c. B = C