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5. For real numbers x and y, recall that max(x, y) is the bigger number between x andy and min(x, y) is the smaller number between x and y. Use a proof by cases to show that if x and y are real numbers, then max(x, y) + min(x, y) = x + y.

5. For real numbers x and y, recall that max(x, y) is the bigger number between x andy and min(x, y) is the smaller number between x and y. Use a proof by cases to show that if x and y are real numbers, then max(x, y) + min(x, y) = x + y.

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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5. For real numbers x and y, recall that max(x, y) is the bigger number between x and y and min(x, y) is the smaller number between x and y. Use a proof by cases to show that if x and y are real numbers, then max(x, y) + min(x, y) = x + y. 6. Prove that x is a rational number if and only if 2x – 1 is a rational number.
Transcribed Image Text:5. For real numbers x and y, recall that max(x, y) is the bigger number between x and y and min(x, y) is the smaller number between x and y. Use a proof by cases to show that if x and y are real numbers, then max(x, y) + min(x, y) = x + y. 6. Prove that x is a rational number if and only if 2x – 1 is a rational number.
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