Prove or disprove the following statement:
$a \mid b$ and $c \mid d$ implies $(a + c) \mid (b + d)$.
We can disprove it with a counter example.
We take $a=2, b=4$ and $c=1, d=3$, so the premises are true $2 \mid 4$ and $1 \mid 3$.
However, $(a + c) \mid (b + d)$ is $3 \mid 7$, which is false.