How to Symbolize Quantifiers and Predicates in Logic Problems

[nicnicman]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

O(x): x is odd
domain for x is all integers
∀xO(2x + 1)

Would this be correct?

 

[nicnicman]

I got an answer for this from another member of the forum

Domain for x is all integers
O(x): x is odd
∀x∀y((y=2x + 1) → O(y))