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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.

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

parsiad
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  • I'm not sure of understand what you mean by convincing myself. If I say negation even(x) = odd(x) right ? –  Sep 08 '15 at 00:02
  • @Astroman par just means go back to the definitions. A number is called "even" iff $\underline{\qquad}$ and a number is called "odd" iff $\underline{\qquad}$. – Graham Kemp Sep 08 '15 at 00:06
  • Oh, but for what I have to do I don't have to go through all of this. It's not asked. –  Sep 08 '15 at 00:08
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    You asked if "not even" means "odd." You'll have to do some work to prove it, or just take it as given. – parsiad Sep 08 '15 at 00:09
  • Yes, I understand what you mean. I just meant that in my case, I can take it as given and don't need to prove it. Thank you! –  Sep 08 '15 at 00:10