Question

A set O consists of all odd numbers. Use set-builder notation to define O.

Answer 1

You can either list the elements (or list the first to show the underlying pattern, if the elements are too many) or define the set by showing the properties of its elements.

So, you can either say

$O = \{ x | x \text{ is odd} \}$

Or list some of them to make the reader understand: if you're interested in positive odd numbers alone, then option B is ok. If you mean odd integers, instead, you should have written

$O = \{ \ldots,\ -5,\ -3,\ -1,\ 1,\ 3,\ 5,\ldots\}$