Symbolizing Quantified Statements in Logic

[nicnicman]

For a homework assignment I got the following as a question:

Symbolize the following using quantifiers, predicates and logical connectives.

For all integers n, 2n+1 is an odd integer.

Here is what I came up with:

O(x): x is odd
∀x((2x + 1) → O(x))

Would this be the correct form?

Thanks

 

[nicnicman]

What I posted doesn't seem right. Maybe it should be something like this:

O(x): x is odd
∀xO(2x + 1)

Would this be correct?

 

[nicnicman]

Also, the domain of x would be all integers.

 

[Bacle2]

For a homework assignment I got the following as a question:

Symbolize the following using quantifiers, predicates and logical connectives.

For all integers n, 2n+1 is an odd integer.

Here is what I came up with:

O(x): x is odd
∀x((2x + 1) → O(x))

Would this be the correct form?

Thanks

Your transcription says that for all x, if 2x+1, then x is odd. I would use:

Domain is integers, as you said.
O(x): x is odd
∀x∀y((y=2x + 1) → O(y))

 

[nicnicman]

Yeah, that makes more sense. Now it's saying for every integer x, if y = 2x + 1, then y is always odd.

Thanks a lot!