Q3: state whether the following statement are True or False : X 1. The set A = {x ER: x² -5x + 6 ≤ 0} has Max (A) = 3 and Inf (A) = 2 with no minimal element. 2. The open ball B (a; r) in R³ with the respect to metric d(x, y) = x - yll is an open circular disk. 1 /3. The set S = {x € R: x = 1 + (-1)", n € N} is an open set in R. 4. The set of all interior points for the set of natural numbers is N. 5. The interval [0,1] forms an open ball in the metric subspace ([0,1], 1, 1) of the Euclidean space (R,1,1).
Q3: state whether the following statement are True or False : X 1. The set A = {x ER: x² -5x + 6 ≤ 0} has Max (A) = 3 and Inf (A) = 2 with no minimal element. 2. The open ball B (a; r) in R³ with the respect to metric d(x, y) = x - yll is an open circular disk. 1 /3. The set S = {x € R: x = 1 + (-1)", n € N} is an open set in R. 4. The set of all interior points for the set of natural numbers is N. 5. The interval [0,1] forms an open ball in the metric subspace ([0,1], 1, 1) of the Euclidean space (R,1,1).
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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![Q3: state whether the following statement are True or False :
1. The set A = {x ER: x² - 5x + 6 ≤ 0} has Max (A) = 3 and Inf (A) = 2 with no
minimal element.
2. The open ball B(a;r) in R³ with the respect to metric d(x, y) = x - yll is an open
1
circular disk.
(3.
3. The set S = {x € R: x = 1 + (-1)", n = N} is an open set in R.
4. The set of all interior points for the set of natural numbers is N.
5. The interval [0,1] forms an open ball in the metric subspace ([0,1], 1, 1) of the Euclidean
space (R,1,1).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22262945-e5e2-4bf7-bfbb-b667222e90be%2F7b77b31d-2e40-4ac0-b49c-99e27db5d5df%2Fzkwqzja_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q3: state whether the following statement are True or False :
1. The set A = {x ER: x² - 5x + 6 ≤ 0} has Max (A) = 3 and Inf (A) = 2 with no
minimal element.
2. The open ball B(a;r) in R³ with the respect to metric d(x, y) = x - yll is an open
1
circular disk.
(3.
3. The set S = {x € R: x = 1 + (-1)", n = N} is an open set in R.
4. The set of all interior points for the set of natural numbers is N.
5. The interval [0,1] forms an open ball in the metric subspace ([0,1], 1, 1) of the Euclidean
space (R,1,1).
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