A and B be two sets, each one of them having a minimum. Assume that A n B is not ty. Then An B has a minimum. ct one: a. True, it will be either the minimum of A or the minimum of B. b. False, here is a counter-example: A = [0, 1) and B = [1/2, 2]. c. False, here is a counter-example: A = [−1, 0) U (1, 2] and B = [1/2, 2]. d. True, because An B is bounded below (by the minimum of A) and not empty.
A and B be two sets, each one of them having a minimum. Assume that A n B is not ty. Then An B has a minimum. ct one: a. True, it will be either the minimum of A or the minimum of B. b. False, here is a counter-example: A = [0, 1) and B = [1/2, 2]. c. False, here is a counter-example: A = [−1, 0) U (1, 2] and B = [1/2, 2]. d. True, because An B is bounded below (by the minimum of A) and not empty.
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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![Let A and B be two sets, each one of them having a minimum. Assume that An B is not
empty. Then An B has a minimum.
Select one:
a. True, it will be either the minimum of A or the minimum of B.
O b.
False, here is a counter-example: A = [0, 1) and B
=
: [1/2, 2].
c.
False, here is a counter-example: A = [−1, 0) U (1, 2] and B = [1/2, 2].
O d. True, because An B is bounded below (by the minimum of A) and not empty.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3cb672f7-47ed-4ee3-be4e-71db737c6150%2Fb1790afe-065a-45fc-86c3-4179d2c0d075%2Fq4unfmw_processed.png&w=3840&q=75)
Transcribed Image Text:Let A and B be two sets, each one of them having a minimum. Assume that An B is not
empty. Then An B has a minimum.
Select one:
a. True, it will be either the minimum of A or the minimum of B.
O b.
False, here is a counter-example: A = [0, 1) and B
=
: [1/2, 2].
c.
False, here is a counter-example: A = [−1, 0) U (1, 2] and B = [1/2, 2].
O d. True, because An B is bounded below (by the minimum of A) and not empty.
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