Set Notation: Write set of ordered pairs of odd integers

Question

I am trying to write down the set of all ordered pairs $(n,m)$ such that $n=2k+1:k\in\mathbb{Z}^{+}$ and $m=2l+1:l\in\mathbb{Z}^{+}$. How would that be written in set notation?

Answer 1

I would use $$\left\{(n,m)\in \mathbb{Z}^2 \mid \exists k, l \in \mathbb{Z}^+:n=2k+1,m=2l+1\right\}$$

Answer 2

One way is: $$ \{ (2k+1, 2l+1) \mid k, l \in \mathbb{Z}^+ \} $$

Answer 3

one another way is: $$ \{x|\exists y, z\in \Bbb{Z}: x=(y,z) \wedge \exists k, l \in \Bbb{Z}^+: y=2k+1 \wedge z=2l+1\}$$