- #1
mohabitar
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Let n be an integer. Prove that if n + 5 is odd, then 3n + 2 is even.
So the instructions say to use a direct proof. I couldn't 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 that's correct, but how could this be done using a direct proof?
So the instructions say to use a direct proof. I couldn't 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 that's correct, but how could this be done using a direct proof?