1. The problem statement, all variables and given/known data im supposed to use a direct proof to prove that if 1-n^2>0 then 3n-2 is odd for all n∈Z 2. Relevant equations 3. The attempt at a solution if you let n∈z then suppose that 1-n^2>0 then 1>n^2 but the only inter n such that 1>n^2 is 0. 3x0-2=-2 as -2=2(-1), -2 is even . Hence if 1-n^2>0 then 3n-2 is even when n∈z. The part that im confused on is why in the book does it say for directs proofs to choose an arbitrary value for n and prove that Q(X) is true? In this proof I had to prove it the same way but there was no way I could let N represent an arbitrary value. The only value that worked was when n=0.