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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Statements and Logic

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