Let n be an integer. Prove that if n + 5 is odd, then 3n + 2 is even.(adsbygoogle = window.adsbygoogle || []).push({});

So the instructions say to use a direct proof. I couldnt figure that method out, so I used a controposition proof and that seemed to work ok. Here are my contraposition steps:

Assume 3n+2 is odd

Def of odd: n=2k+1

n+5=2k+1+5 = 2k+6 = 2(k+3)

n+5 is even (multiple of 2)

since negation of conclusion implies hypothesis is false, original statement is true.

Im pretty sure thats correct, but how could this be done using a direct proof?

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# Simple Direct Proof

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