Proof by contrapositive: If n is even, then 2(n) is also even.

Question

The contrapositive would be:

If 2(n) is odd, then n is odd.

 

What is wrong with my logic?  The first statement is obviously true, and the second one is obviously false.  I know it must be incorrect to use the contrapositive like this, but why???

Answer 1

You correctly state the contrapositive. 

The hypothesis, if 2(n) is odd, is a false statement (it cannot be). Therefore the conclusion is also false.

Answer 2

Did the question ask you to prove it by contrapostive or was that your choice?