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    Integer Proofs by Contradiction

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    Assume that n is a positive integer. Use the proof by contradiction method to prove:

    (a) If 7n + 4 is an even integer, then n is an even integer.

    (b) Prove: n is an even integer iff 7n + 4 is an even integer.
    (Note this is an if and only if (iff) statement.

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    https://brainmass.com/math/discrete-math/integer-proofs-by-contradiction-115349

    Solution Preview

    Assume that n is a positive integer. Use the proof by contradiction method to prove:

    (a) If 7n + 4 is an even integer, then n is an even integer.

    Proof. We prove it by contradiction. Suppose that n is NOT an even integer. Then n is odd. So, n=2k+1 for some integer k. Thus,
    7n+4=7(2k+1)+4
    ...

    Solution Summary

    Integer proofs by contradiction are provided.

    $2.19