# Integer Proofs by Contradiction

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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#### 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