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6. Use a direct proof to show that the product of two odd numbers is odd. 8. Prove that if n is a perfect square, then n + 2 is not a perifect square 12. Prove or disprove that the product of a nonzero rational number and an irrational number is irrational.

6. Use a direct proof to show that the product of two odd numbers is odd. 8. Prove that if n is a perfect square, then n + 2 is not a perifect square 12. Prove or disprove that the product of a nonzero rational number and an irrational number is irrational.

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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Sure! Here’s the transcription for an educational website: --- **Mathematical Proof Exercises** 1. **Exercise 6:** Use a direct proof to show that the product of two odd numbers is odd. 2. **Exercise 8:** Prove that if \( n \) is a perfect square, then \( n + 2 \) is not a perfect square. 3. **Exercise 12:** Prove or disprove that the product of a nonzero rational number and an irrational number is irrational. --- These exercises are designed to help develop skills in mathematical reasoning and proof techniques.
Transcribed Image Text:Sure! Here’s the transcription for an educational website: --- **Mathematical Proof Exercises** 1. **Exercise 6:** Use a direct proof to show that the product of two odd numbers is odd. 2. **Exercise 8:** Prove that if \( n \) is a perfect square, then \( n + 2 \) is not a perfect square. 3. **Exercise 12:** Prove or disprove that the product of a nonzero rational number and an irrational number is irrational. --- These exercises are designed to help develop skills in mathematical reasoning and proof techniques.
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