Disprove $ \phi (m + n) = \phi (m) + \phi (n)$ where $m$ and $n$ are natural numbers.
We will use a counter-example to disprove the statement.
Consider the smallest natural numbers $m=1$ and $n=1$. Then
$$ \begin{align} \phi(1 + 1) = \phi(2) = 1 \quad & \ne \quad 2 = 1 + 1 = \phi(1) + \phi(1) \\ \\ \phi(1 + 1) \quad & \ne \quad \phi(1) + \phi(1) \end{align} $$
That is, $n=m=1$ is a counter-example.