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Problem 21: (Integers Cannot Be Both Even And Odd)

Let $x$ be an integer. Prove each of the following implications is true. Don't forget to use the definitions of even and odd from the first day of class.

  1. If $x$ is even, then $x$ is not odd. (Hint: Prove that the negation is false.)
  2. If $x$ is odd, then $x$ is not even. (Hint: What is the contrapositive of the first implication?)

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