Predicate that indicates if a number is even or not.

Question

So I'm kinda new to predicates and there was something that I was wondering. If I have the following predicate: $\text{even}(x) : x$ is an even number. And let's say I want to test if a number is odd, does the negation of $\text{even}(x)$ achieve this goal? I don't want to use the $\text{even}$ predicate, but something else to test if my number is odd or not.

Thanks.

Answer 1

Yes. However, to arrive at this, you should convince yourself that a natural number is either even or odd.