Question

Suppose you are allowed to give either a direct proof or a proof by contraposition of the following: if 3n + 5 is even, then n is odd. Which type of proof would be easier to give? Explain why

Answer 1

Answer:

Note that n2(1+n)=2k+1 does not imply that either n2=2k+1 or n+1=2k+1. Also,

√

2k+1

is sometimes an integer, let k=4 for example. And you are not trying to prove that n is even, you are trying to prove that n2+n3 is even