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Using either proof by contraposition or proof by contradiction, show that: if n2 + n is...

  1. Using either proof by contraposition or proof by contradiction, show that:

    if n2 + n is irrational, then n is irrational.
  2. Using the definitions of odd and even show that the following 4 statements are equivalent:
    1. n2 is odd
    2. 1 − n is even
    3. n3 is odd
    4. n + 1 is even
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