4. Consider the inequality | r – 2 K 1 ,V rE R. Which of the following solutions satisfies the inequality? I. {r €R:r<1 and r> 3} II. {r ER :r € [1, 3]} III. (r €R:1

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Chapter2: Second-order Linear Odes
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4. Consider the inequality | x – 2 |< 1 ,V r €R. Which of the following solutions
satisfies the inequality?
I. {r €R: r <1 and r > 3}
A. I only
II. {r € R :1 € [1, 3]} III. (x ER: 1< x < 3)
B. II and III only
С. I only.
D. I, II and III
E. None of the above choices A, B,C or D.
5. Let A and B be nonempty subsets of R. Which of the following best qualifies the
pair (A, B) as a Dedekind cut?
I. AnB+0
A. I and II only
B. I and III only
II. AUB = R
III. A + 0 andB+0
С. 1, I and II
D. III only
E. None of the above choices A, B,C or D.
K. Piesie.
Page 2 of 8
6. Which of the following best define(s) the triangle inequality?
I. | a + b|<|a | + |6| II. | a + b | S|a|+[b[|
III. | a + b|2|a |+|6|
A. II only
B. I and II only
C. I only
D. II and III only
E. None of the above choices A, B,C or D
Transcribed Image Text:4. Consider the inequality | x – 2 |< 1 ,V r €R. Which of the following solutions satisfies the inequality? I. {r €R: r <1 and r > 3} A. I only II. {r € R :1 € [1, 3]} III. (x ER: 1< x < 3) B. II and III only С. I only. D. I, II and III E. None of the above choices A, B,C or D. 5. Let A and B be nonempty subsets of R. Which of the following best qualifies the pair (A, B) as a Dedekind cut? I. AnB+0 A. I and II only B. I and III only II. AUB = R III. A + 0 andB+0 С. 1, I and II D. III only E. None of the above choices A, B,C or D. K. Piesie. Page 2 of 8 6. Which of the following best define(s) the triangle inequality? I. | a + b|<|a | + |6| II. | a + b | S|a|+[b[| III. | a + b|2|a |+|6| A. II only B. I and II only C. I only D. II and III only E. None of the above choices A, B,C or D
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