**Problem 13:**Let \( S \) be the statement: The product of any irrational number and any nonzero rational number is irrational.a. **Write a negation for \( S \).****Answer:**Negation for \( S \): There exist an irrational number and a nonzero rational number whose product is rational.b. **Prove \( S \) by contradiction.**

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Answered: 13. Let S be the statement: The product…

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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13. Let S be the statement: The product of any irrational number and any nonzero rational number is irrational. a. Write a negation for S. Answer + Negation for S: There exist an irrational number and a nonzero rational number whose product is rational. b. Prove S by contradiction.