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21. Which of the following is/are a mll set? 1. (r:z is prime and 7

21. Which of the following is/are a mll set? 1. (r:z is prime and 7

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.1: Sets And Geometry
Problem 19E: What relationship subset, intersect, disjoint, or equivalent can be used to characterize the two...
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E. None of the above. 21. Which of the following is/are a null set? I. {r:r is prime and 7 << 10} A. I and II only II. {r:r€ 0} II. {r € N: 0< 1 < 1} В. 1 only C. II and III only D. III only E. None of the above choices A, B, C, or D. 22. Which of these statements is/are not true? I. Every decreasing sequence of positive integers has a finite number of terms. II. Every bounded sequence in R is convergent. III. Every monotonic increasing sequence of real numbers is convergent. A. I only B. I and II only С. I аnd II оnly D. I, II and III E. None of the above choices A, B, C, or D. 23. Find sup A if A -{ :z EIR be a bounded subset of R. A. В. - C. 1+ v2 D. 1- V2 E. None of the above. K. Piesie. Page 6 of 8 24. Which of these statements is /are not true? I. Every bounded subset of R always contains its lower and upper bounds. II. The infimum and the supremum of any bounded subset of R are unique. III. Every monotonic decreasing sequence of real numbers that is bounded below converges to its infimum. A I and II only B. II and III only C. I, II and III D. III only E. None of the above choices A, B, C or D. 25. Let a, :- (), n>1 Which of these conditions must be met if a, is to converge to 1? I. for any e > 0, n >. II. for any e > 0, ke vn 2 n(e).. II. for any e > 0, | >e V n 2 n(e).. A I and II only В. 1 only C. II and III only D. I and III only E. None of the above choices A, B, C or D.. 26. A sequence a, is defined inductively by a = 2 and an+1 -, n2 1. If a, is decreasing and bounded below, find the limit of a,. A. (3+ V5) B. (3+ V3) C. (3 – V5) D. V5 E. None of the above.
Transcribed Image Text:E. None of the above. 21. Which of the following is/are a null set? I. {r:r is prime and 7 << 10} A. I and II only II. {r:r€ 0} II. {r € N: 0< 1 < 1} В. 1 only C. II and III only D. III only E. None of the above choices A, B, C, or D. 22. Which of these statements is/are not true? I. Every decreasing sequence of positive integers has a finite number of terms. II. Every bounded sequence in R is convergent. III. Every monotonic increasing sequence of real numbers is convergent. A. I only B. I and II only С. I аnd II оnly D. I, II and III E. None of the above choices A, B, C, or D. 23. Find sup A if A -{ :z EIR be a bounded subset of R. A. В. - C. 1+ v2 D. 1- V2 E. None of the above. K. Piesie. Page 6 of 8 24. Which of these statements is /are not true? I. Every bounded subset of R always contains its lower and upper bounds. II. The infimum and the supremum of any bounded subset of R are unique. III. Every monotonic decreasing sequence of real numbers that is bounded below converges to its infimum. A I and II only B. II and III only C. I, II and III D. III only E. None of the above choices A, B, C or D. 25. Let a, :- (), n>1 Which of these conditions must be met if a, is to converge to 1? I. for any e > 0, n >. II. for any e > 0, ke vn 2 n(e).. II. for any e > 0, | >e V n 2 n(e).. A I and II only В. 1 only C. II and III only D. I and III only E. None of the above choices A, B, C or D.. 26. A sequence a, is defined inductively by a = 2 and an+1 -, n2 1. If a, is decreasing and bounded below, find the limit of a,. A. (3+ V5) B. (3+ V3) C. (3 – V5) D. V5 E. None of the above.
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