**Determine whether the proposed negation is correct. If it is not, write a correct negation.**---**Statement:** The product of any irrational number and any rational number is irrational.**Proposed negation:** The product of any irrational number and any rational number is rational.---1. ⃝ The proposed negation is correct.2. ⃝ The proposed negation is not correct. A possible correct negation would be: There is an irrational number and a rational number whose product is rational.3. ⃝ The proposed negation is not correct. A possible correct negation would be: There is not an irrational number and a rational number whose product is rational.4. ⃝ The proposed negation is not correct. A possible correct negation would be: There exists an irrational product of an irrational number and a rational number.5. ⃝ The proposed negation is not correct. A possible correct negation would be: There does not exist an irrational product of any irrational number and any rational number.

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Description: **Determine whether the proposed negation is correct. If it is not, write a correct negation.**---**Statement:** The product of any irrational number and any rational number is irrational.**Proposed negation:** The product of any irrational number a

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Determine whether the proposed negation is correct. If it is not, write a correct negation. Statement: The product of any irrational number and any rational number is irrational. Proposed negation: The product of any irrational number and any rational number is rational. The proposed negation is correct. The proposed negation is not correct. A possible correct negation would be: There is an irrational number and a rational number whose product is rational. The proposed negation is not correct. A possible correct negation would be: There is not an irrational number and a rational number whose product is rational. The proposed negation is not correct. A possible correct negation would be: There exists an irrational product of an irrational number and a rational number. The proposed negation is not correct. A possible correct negation would be: There does not exist an irrational product of any irrational number and any rational number.

Determine whether the proposed negation is correct. If it is not, write a correct negation. Statement: The product of any irrational number and any rational number is irrational. Proposed negation: The product of any irrational number and any rational number is rational. The proposed negation is correct. The proposed negation is not correct. A possible correct negation would be: There is an irrational number and a rational number whose product is rational. The proposed negation is not correct. A possible correct negation would be: There is not an irrational number and a rational number whose product is rational. The proposed negation is not correct. A possible correct negation would be: There exists an irrational product of an irrational number and a rational number. The proposed negation is not correct. A possible correct negation would be: There does not exist an irrational product of any irrational number and any rational number.

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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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

Topic Video

Question

**Determine whether the proposed negation is correct. If it is not, write a correct negation.**

---

**Statement:** The product of any irrational number and any rational number is irrational.

**Proposed negation:** The product of any irrational number and any rational number is rational.

---
1. ⃝ The proposed negation is correct.

2. ⃝ The proposed negation is not correct. A possible correct negation would be: There is an irrational number and a rational number whose product is rational.

3. ⃝ The proposed negation is not correct. A possible correct negation would be: There is not an irrational number and a rational number whose product is rational.

4. ⃝ The proposed negation is not correct. A possible correct negation would be: There exists an irrational product of an irrational number and a rational number.

5. ⃝ The proposed negation is not correct. A possible correct negation would be: There does not exist an irrational product of any irrational number and any rational number.

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