3.7.21. Write the negation of the following statements without using the negation symbol . Also, for each statement, decide whether it is true or false. Explain your answer briefly. (a) (Vr E R)(3y E R)(r > y)
3.7.21. Write the negation of the following statements without using the negation symbol . Also, for each statement, decide whether it is true or false. Explain your answer briefly. (a) (Vr E R)(3y E R)(r > y)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
3.7.21
A)
![(a) For all r E A there is a bE B such that b> r.
(b) For any positive real number r, there is a natural number n, for which <r.
3.7.21. Write the negation of the following statements without using the negation symbol
Also, for each statement, decide whether it is true or false. Explain your answer briefly.
(a) (Vr E R)(3y E R)(r > y)
(b) (3r € Z) [(r = (r+ 1)*) → (r³ € Z)]
©2017 Shay Fuchs. All rights reserved.
79
3.7. EXERCISES FOR CHAPTER 3
CHAPTER 3. INFORMAL LOC
(c) (Vn E N)((n- 1)° + n° + (n + 1)*)
(d) [(Vz ER)(z > 0)) (Vr E R)( =+1)]
(e) (Vr ER)( (z2 <-1) (a+ 1)2 a² + 1]]
(f) (z E R)(r >0) (3n E N)(n-z> 1)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb149039b-c609-4874-85d1-64f29a0551b7%2F568c04aa-a63c-4f6e-9b0e-61e719234b0b%2Fl9qpgoa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) For all r E A there is a bE B such that b> r.
(b) For any positive real number r, there is a natural number n, for which <r.
3.7.21. Write the negation of the following statements without using the negation symbol
Also, for each statement, decide whether it is true or false. Explain your answer briefly.
(a) (Vr E R)(3y E R)(r > y)
(b) (3r € Z) [(r = (r+ 1)*) → (r³ € Z)]
©2017 Shay Fuchs. All rights reserved.
79
3.7. EXERCISES FOR CHAPTER 3
CHAPTER 3. INFORMAL LOC
(c) (Vn E N)((n- 1)° + n° + (n + 1)*)
(d) [(Vz ER)(z > 0)) (Vr E R)( =+1)]
(e) (Vr ER)( (z2 <-1) (a+ 1)2 a² + 1]]
(f) (z E R)(r >0) (3n E N)(n-z> 1)]
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