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

Prove or disprove each of the following statements. To disprove just give a counter example.   Believe the statement is true but not sure how to prove it 2 can be represented as 4 irrational numbers by sqrt(2) * 1/sqrt(2) * 2sqrt(2) * 1/sqrt(2)

Write the following statement as a mathematical statement. Use variable names to denote arbitrary numbers in the domain. Your statements and should be expressed using algebra. "There is no largest integer."