Ok, the problem is this:

Provide a specific counterexample that shows the statement is false.

Statement: for all function f and g on N, if , then .

I've chosen and as this seems fairly obvious.

It is easy to show that is in ...though this is not accurate, it still holds. I much pick values for N and K such that:

so I choose K = 1 and N = 2

The second one, I am trying a proof by contradiction (though I was always told to assume the negation of the hypothesis). If we simply do the same thing we get:

, choose n = 2K and we get

which is false, so the original statement must be false. Is this a correct way to do this?