$a + b < \min(a,b) \Leftrightarrow a < 0 \and b < 0$

If both a and b are negative, $a + b < min(a, b)$. For example

     $a = -5$
$b = -7$
$a+ b = -5 + (-7) = -12$
$min(-5, -7) = -7$