State whether the following statements are true or false:
$(1)$ Severe respiratory diseases in children are caused by $NO_2$ gas.
$(2)$ Carbon monoxide binds with hemoglobin in the blood to form a carboxyhemoglobin complex.
$(3)$ The carboxyhemoglobin complex is $100$ times more stable than the oxygen-hemoglobin complex.
$(4)$ The $pH$ of rainwater is around $5.6$.

(C) $(1)$ True: $NO_2$ is a respiratory irritant that can cause lung damage in children.
$(2)$ True: $CO$ binds to hemoglobin to form carboxyhemoglobin.
$(3)$ False: The carboxyhemoglobin complex is about $300$ times more stable than the oxygen-hemoglobin complex,not $100$ times.
$(4)$ True: Normal rainwater has a $pH$ of approximately $5.6$ due to the dissolution of atmospheric $CO_2$.