Please answer the following questions. By dragging statements from the left column to the right column below, construct a valid proof of the statement:**For all integers n, if 13n is even, then n is even.**The correct proof will use 3 of the statements below.**Statements to choose from:**1. Let n be an arbitrary integer and assume n is odd.2. Let n be an arbitrary integer and assume n is even.3. Since 13 is odd and the product of an odd number and an even number is even,4. Let n be an arbitrary integer and assume 13n is even.5. 13n must be even.6. Since 13 is odd and the product of odd numbers is odd,7. 13n must be odd.8. n must be even.9. Since an even number divided by 13 must be even,**Your Proof:** Put chosen statements in order in this column and press the Submit Answers button. **Interactive Proof Exercise: Proving a Mathematical Statement**For any integer \( n \), if \( n \) is even, then \( 17n \) is even.**Instructions:**By dragging statements from the left column to the right column, construct a valid proof of the statement. The correct proof will use 3 of the statements provided.**Statements to choose from:**1. \( n \) must be even.2. Let \( n \) be an arbitrary integer and assume \( n \) is even.3. \( 17n \) must be odd.4. Since an even number divided by 17 must be odd,5. Since 17 is odd and the product of an odd number and an odd number is odd,6. Since the product of any number with an even number is even,7. Let \( n \) be an arbitrary integer and assume \( 17n \) is even.8. Let \( n \) be an arbitrary integer and assume \( 17n \) is odd.9. \( 17n \) must be even.**Your Proof:**Put the chosen statements in order in the space provided and press the Submit Answers button to check your logic and assumptions.

Answered: Image /qna-images/answer/3973b086-f90a-4e72-a395-6f9eed68d18e.jpg

By dragging statements from the left column to the right column below, construct a valide proof of the statement: For all integers n, if 13n is even, then n is even. The correct proof will use 3 of the statements below. Statements to choose from: Let n be an arbitrary integer and assume n is odd. Let n be an arbitrary integer and assume n is even. Since 13 is odd and the product of an odd number and an even number is even, Let n be an arbitrary integer and assume 13n is even. 13n must be even Since 13 is odd and the product of odd numbers is odd, 13n must be odd. n must be even Since an even number divided by 13 must be even, Your Proof: Put chosen statements in order in this column and press the Submit Answers button.

By dragging statements from the left column to the right column below, construct a valide proof of the statement: For all integers n, if 13n is even, then n is even. The correct proof will use 3 of the statements below. Statements to choose from: Let n be an arbitrary integer and assume n is odd. Let n be an arbitrary integer and assume n is even. Since 13 is odd and the product of an odd number and an even number is even, Let n be an arbitrary integer and assume 13n is even. 13n must be even Since 13 is odd and the product of odd numbers is odd, 13n must be odd. n must be even Since an even number divided by 13 must be even, Your Proof: Put chosen statements in order in this column and press the Submit Answers button.

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

Please answer the following questions.

By dragging statements from the left column to the right column below, construct a valid proof of the statement:

**For all integers n, if 13n is even, then n is even.**

The correct proof will use 3 of the statements below.

**Statements to choose from:**

1. Let n be an arbitrary integer and assume n is odd.
2. Let n be an arbitrary integer and assume n is even.
3. Since 13 is odd and the product of an odd number and an even number is even,
4. Let n be an arbitrary integer and assume 13n is even.
5. 13n must be even.
6. Since 13 is odd and the product of odd numbers is odd,
7. 13n must be odd.
8. n must be even.
9. Since an even number divided by 13 must be even,

**Your Proof:** Put chosen statements in order in this column and press the Submit Answers button.

**Interactive Proof Exercise: Proving a Mathematical Statement**

For any integer \( n \), if \( n \) is even, then \( 17n \) is even.

**Instructions:**

By dragging statements from the left column to the right column, construct a valid proof of the statement. The correct proof will use 3 of the statements provided.

**Statements to choose from:**

1. \( n \) must be even.
2. Let \( n \) be an arbitrary integer and assume \( n \) is even.
3. \( 17n \) must be odd.
4. Since an even number divided by 17 must be odd,
5. Since 17 is odd and the product of an odd number and an odd number is odd,
6. Since the product of any number with an even number is even,
7. Let \( n \) be an arbitrary integer and assume \( 17n \) is even.
8. Let \( n \) be an arbitrary integer and assume \( 17n \) is odd.
9. \( 17n \) must be even.

**Your Proof:**

Put the chosen statements in order in the space provided and press the Submit Answers button to check your logic and assumptions.

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