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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
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.
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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