# hw4 - Homework 4 Q1 Exercise 4 d p 167 a0=2 a1=0 a2=8 a3=0...

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Homework 4 Q1. Exercise 4, d), p. 167 a 0 =2 a 1 =0 a 2 =8 a 3 =0 Q2. Exercise 12, c), p. 168 −3 · (−4) n-1 + 4 · (−4) n-2 = −3 · (−4) n-1 − (−4) · (−4) n-2 = (−3 − 1) · (−4) n-1 = (−4) n Q3. Exercise 16, b), p. 168 F(n) = 1+ 3 n Q4. Exercise 26, a), p. 169 The first term is 3 The next term is obtained by using the formula 2n − 1 Or by using 2n + 2 Q5. Exercise 32, b), p. 169 (1 − 1) + (3 − 2) + (9 − 4) + (27 − 8) + (81 − 16) + (243 − 32) + (729 − 32) + (2189 − 64) + (6561 − 128) = 9330 Q6. Exercise 34, a), p.169 (1 - 1) + (1 - 2) + (2 - 1) + (2 - 2) + (3 - 1) + (3 - 2) = 3 ABET 5 - Cardinality of Sets Q7. Exercise 2, a), p. 176 N= {11, 12, 13, 14, ...} f: Z>10 -> N

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f(n) = n + 11 z <-> z – 11 which is a bijection Hence, it is countably infinite Q8. Exercise 2, e), p. 176 f : {2, 3} × Z>0 ->N (n, z) <-> 2(z − 1) if n = 2, 2(z − 1) + 1 if n = 3, is bijective Hence, it is countable Q9. Exercise 4, a), p. 176 Countable because the integers not divisible by 3 are a subset of the integer Q10. Exercise 6, p. 176 If you move the guest in room n to room n+2 then the guest can remain in the hotel Q11. Exercise 10, b), p. 176 A = (0, 1) N B = (0, 1) A − B = N is countably infinite Q12. Exercise 16, p. 176 2 Let A be a countable set.
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