How do I represent this statement using symbolic notation?
This is my attempt at it.
$$
\forall n \in \Bbb{Z}, \forall m \in \Bbb{Z}, (n = 2q + 1) \wedge (m = 2k + 1) \Longrightarrow (m + n = 2l)
$$
In English, I would read it as:
For all $n$ in the set of integers, and for all $m$ in the set of integers, if $n$ is odd and $m$ is odd, then $m + n$ is even.
Is this the right way to show it symbolically?
Best Answer
Rather: $$ \forall n \in \Bbb{Z}, \forall m \in \Bbb{Z} \Big(\big(\exists q\in\mathbb Z (n = 2q + 1)\big) \wedge \big(\exists k\in\mathbb Z(m = 2k + 1)\big) \Longrightarrow \exists \ell\in\mathbb Z(m + n = 2\ell)\Big) $$ Note. Final version improved according to the suggestions of Henning Makholm.