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2. Consider the following statement: "if A, B are two non-empty sets, each one having a minimum, then AUB has a minimum" Determine if this statement is true or false. If it is true, give a proof. If it is false, provide a counter-example. (Note: the solution is not very long and does not require the usage of complicated calculations; it can therefore be typed using plain text, with minimal mathematical notations, as per the instructions provided in the lecture notes. You do not have to present your solution this way, but it can help you train for the "short response" questions in the final exam.)

2. Consider the following statement: "if A, B are two non-empty sets, each one having a minimum, then AUB has a minimum" Determine if this statement is true or false. If it is true, give a proof. If it is false, provide a counter-example. (Note: the solution is not very long and does not require the usage of complicated calculations; it can therefore be typed using plain text, with minimal mathematical notations, as per the instructions provided in the lecture notes. You do not have to present your solution this way, but it can help you train for the "short response" questions in the final exam.)

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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2. Consider the following statement: "if A, B are two non-empty sets, each one having a minimum, then AUB has a minimum". Determine if this statement is true or false. If it is true, give a proof. If it is false, provide a counter-example. (Note: the solution is not very long and does not require the usage of complicated calculations; it can therefore be typed using plain text, with minimal mathematical notations, as per the instructions provided in the lecture notes. You do not have to present your solution this way, but it can help you train for the "short response" questions in the final exam.)
Transcribed Image Text:2. Consider the following statement: "if A, B are two non-empty sets, each one having a minimum, then AUB has a minimum". Determine if this statement is true or false. If it is true, give a proof. If it is false, provide a counter-example. (Note: the solution is not very long and does not require the usage of complicated calculations; it can therefore be typed using plain text, with minimal mathematical notations, as per the instructions provided in the lecture notes. You do not have to present your solution this way, but it can help you train for the "short response" questions in the final exam.)
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