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Hint: it is sufficient to show A implies B, B implies C, C implies D, and...

Hint: it is sufficient to show A implies B, B implies C, C implies D, and D implies A, as repeated application of the hypothetical syllogism will give you A iff B iff C iff D.

  1. 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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