A number $n$ is called even if $n\%2 = 0$. An odd number $m$ is odd if $m \%2 \neq 0$. Futhermore lets write an $m$ as $m=2q+1$ and $n$ = $n = 2p$ for $p,q\in \mathbb{R}$
The sum of an odd number $m$ and an even number $n$ is always odd.
Lets write $m = 2q+1$ and $n = 2p$. $\implies$ $m+n$ = $2q+2p + 1$ = $2(p+q) + 1$. We know $2(p+q) %2 = 0$ but $1\%2 \neq0$ $\implies$ $m+n$ must be odd.