3.7.19. Write the statement "There is no set A, for which A E A", without using words of negation (e.g., 'no', 'not').
3.7.19. Write the statement "There is no set A, for which A E A", without using words of negation (e.g., 'no', 'not').
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
3.7.19 only
![3.7.19. Write the statement "There is no set A, for which A E A", without using words of negation (e.g.,
'no', 'not').
3.7.20. Negate the following statements. You may use words or the logic symbols in your answers. Simplify
the negations as much as you can.
(a) For all rE A there is a be B such that b> r.
1
(b) For any positive real number r, there is a natural number n, for which
<z.
< x.
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) (Vz E R)(3y e R)(x² > y²)
(b) (3r E Z) [(x2 = (x+1)2) = ( e Z)]
©2017 Shay Fuchs. All rights reserved.
79
3.7. EXERCISES FOR CHAPTER 3
CHAPTER 3. INFORMAL LOGIC](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F456c652e-48e0-467a-a300-ab3698edfbc3%2Ff6a4f585-8e57-40f8-941b-a18c90f71236%2Fs511iji_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3.7.19. Write the statement "There is no set A, for which A E A", without using words of negation (e.g.,
'no', 'not').
3.7.20. Negate the following statements. You may use words or the logic symbols in your answers. Simplify
the negations as much as you can.
(a) For all rE A there is a be B such that b> r.
1
(b) For any positive real number r, there is a natural number n, for which
<z.
< x.
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) (Vz E R)(3y e R)(x² > y²)
(b) (3r E Z) [(x2 = (x+1)2) = ( e Z)]
©2017 Shay Fuchs. All rights reserved.
79
3.7. EXERCISES FOR CHAPTER 3
CHAPTER 3. INFORMAL LOGIC
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