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Suppose A and B are non-empty sets of real numbers that are both bounded above. (a) Prove that, if AC B, then sup A< sup B. (b) Prove that sup AUB = max{sup A, sup B}. (c) Prove that, if AnB +0, then sup ANB < min{sup A, sup B}. Give an example to show that equality need not hold.

Suppose A and B are non-empty sets of real numbers that are both bounded above. (a) Prove that, if AC B, then sup A< sup B. (b) Prove that sup AUB = max{sup A, sup B}. (c) Prove that, if AnB +0, then sup ANB < min{sup A, sup B}. Give an example to show that equality need not hold.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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A solid theorem and proof these questions please, I cannot figure out how

Suppose A and B are non-empty sets of real numbers that are both bounded above. (a) Prove that, if AC B, then sup A< sup B. (b) Prove that sup AUB = max{sup A, sup B}. (c) Prove that, if AnB #0, then sup ANB < min{sup A, sup B}. Give an example to show that equality need not hold.
Transcribed Image Text:Suppose A and B are non-empty sets of real numbers that are both bounded above. (a) Prove that, if AC B, then sup A< sup B. (b) Prove that sup AUB = max{sup A, sup B}. (c) Prove that, if AnB #0, then sup ANB < min{sup A, sup B}. Give an example to show that equality need not hold.
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