# Every natural number is odd or even - logical expression

#### logicstudent123

##### New member
Hello,

I am not really sure in which thread to post this nor where to find help for this question so I am trying here. This may seem as a simple question but I got lost in the syntax and wanted to make sure if I'm doing this right.

Please have a look at the question in the picture, it is my question from recent logic exam and I wanted to check if my answer was correct.

First 2 are the same thing just different syntax right? And the 3rd one is incorrect (wrong interpretation) in my opinion. Which of these is correct?

Thank you!

#### pka

##### Elite Member
I first taught a university level course in symbolic in 1967 using Erv Copi's text. I taught such courses regularly.
That said, I have really have no idea what syntactically incorrect means. As far as I know it is not a construct mathematical logicians use.
I can give you a symbolic formula in the universe of natural numbers $$(\forall n)(\exists k)\left[n=2k\vee n=2k+1\right]$$.

#### Dr.Peterson

##### Elite Member
First 2 are the same thing just different syntax right? And the 3rd one is incorrect (wrong interpretation) in my opinion. Which of these is correct?

Thank you!View attachment 21660
The last is incorrect in meaning, as you say.

Are you saying the first two have valid syntax though they are different, or that one has invalid syntax?

#### logicstudent123

##### New member
The last is incorrect in meaning, as you say.

Are you saying the first two have valid syntax though they are different, or that one has invalid syntax?
I don't have the right answer to this question so that's what I'm trying to figure out.. I thought first two are both correct in meaning but one of those has invalid syntax. But it doesn't have to be that way, that was just my interpretation.

#### Dr.Peterson

##### Elite Member
I don't have the right answer to this question so that's what I'm trying to figure out.. I thought first two are both correct in meaning but one of those has invalid syntax. But it doesn't have to be that way, that was just my interpretation.
I'm asking for your interpretation, not for the "right answer"! Our practice here is to ask for your own work, so we know where you need help, or if you're right and we can just commend you.

So which one do you think has invalid syntax, and why? You're probably right ... (though technically a statement with invalid syntax doesn't have a meaning at all, so it can't be correct).

#### pka

##### Elite Member
I don't have the right answer to this question so that's what I'm trying to figure out.. I thought first two are both correct in meaning but one of those has invalid syntax. But it doesn't have to be that way, that was just my interpretation.
As I posted in reply #2, it seems to me that you are a prisoner of your test-book/lecture-notes.
We do not have access to either of those. If you tell us the name of the textbook you are using one of us may know of it.