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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.

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.

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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**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.**
Transcribed Image Text:**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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