Mathmetical resoning. Question 3 please. By controdiaction，contrapositive，or whatever can solve this logically 1. Prove by contradiction that \(6n + 5\) is odd for all integers \(n\).2. Prove that for all integers \(n\), if \(3n + 5\) is even then \(n\) is odd. (Hint: prove the contrapositive)3. Prove that \[|x + y| \leq |x| + |y|\]for all real numbers \(x\) and \(y\).

Answered: 3. Prove that |x+ y| < |x| + \y] for…

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3. Prove that |x+ y| < |x| + \y] for all real numbers x and y.

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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Question

Mathmetical resoning. Question 3 please. By controdiaction，contrapositive，or whatever can solve this logically

1. Prove by contradiction that \(6n + 5\) is odd for all integers \(n\).

2. Prove that for all integers \(n\), if \(3n + 5\) is even then \(n\) is odd. (Hint: prove the contrapositive)

3. Prove that

\[
|x + y| \leq |x| + |y|
\]

for all real numbers \(x\) and \(y\).

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