Below is a statement of a theorem and a proof by contrapositive with some parts of the argument replaced by capital letters. Theorem: For every positive integer x, if x³ is even, then x is even. Proof by contrapositive. Let x be a positive integer. ASsume A. We will prove that B. If x is odd, then it can be written as Cfor some integer k. Plug in the expressionn for x into x³ to get D. The expression for x³ can be written as E. Since (4k3 + 6k² + 3k) is an integer, we can conclude that x³ is odd. What is the correct expression for D? 2k3 + 13 8k3 + 6k2 + 12k + 1

Below is a statement of a theorem and a proof by contrapositive with some parts of the argument replaced by capital letters. Theorem: For every positive integer x, if x³ is even, then x is even. Proof by contrapositive. Let x be a positive integer. ASsume A. We will prove that B. If x is odd, then it can be written as Cfor some integer k. Plug in the expressionn for x into x³ to get D. The expression for x³ can be written as E. Since (4k3 + 6k² + 3k) is an integer, we can conclude that x³ is odd. What is the correct expression for D? 2k3 + 13 8k3 + 6k2 + 12k + 1

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Description: Below is a statement of a theorem and a proof by contrapositive with some parts of the argument replaced by capital letters.Theorem: For every positive integer x, if x³ is even, then x is even.Proof by contrapositive.Let x be a pos itive integer. As

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

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Below is a statement of a theorem and a proof by contrapositive with some parts of the argument replaced by capital letters.
Theorem: For every positive integer x, if x³ is even, then x is even.
Proof by contrapositive.
Let x be a pos itive integer. Assume A. We will prove that B.
If x is odd, then it can be written as Cfor some integer k. Plug in the expressionn for x into x to get D. The expression for x³ can be written as E.
Since (4k + 6k² +3k) is an integer, we can conclude that x³ is odd.
What is the correct expression for D?
O 2k3 + 13
8k3 + 6k2 + 12k + 1
O 8k3 + 12k? + 6k + 1
O 8k3
O 12k2

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