The law of multiple proportions was proposed by

Statement $1$: The mass ratio of hydrogen to oxygen in water obtained from rivers,wells,lakes,or seas is always $1:8$.
Statement $2$: In $1799$,the scientist Joseph Proust proposed the Law of Definite Proportions.

Which of the following pairs of substances illustrate the law of multiple proportions?

To check the principle of multiple proportions,a series of pure binary compounds $(P_m Q_n)$ were analyzed and their composition is tabulated below. The correct option$(s)$ is(are)

Compound	Weight $\%$ of $P$	Weight $\%$ of $Q$
$1$	$50$	$50$
$2$	$44.4$	$55.6$
$3$	$40$	$60$

$(A)$ If empirical formula of compound $3$ is $P_3 Q_4$,then the empirical formula of compound $2$ is $P_3 Q_5$.
$(B)$ If empirical formula of compound $3$ is $P_3 Q_2$ and atomic weight of element $P$ is $20$,then the atomic weight of $Q$ is $45$.
$(C)$ If empirical formula of compound $2$ is $PQ$,then the empirical formula of the compound $1$ is $P_5 Q_4$.
$(D)$ If atomic weight of $P$ and $Q$ are $70$ and $35$,respectively,then the empirical formula of compound $1$ is $P_2 Q$.

When $0.32 \ g$ of sulfur is burnt in air,$224 \ mL$ of $SO_2$ is obtained at $N.T.P$. In another experiment,$SO_2$ is formed by the decomposition of a compound containing $50\%$ sulfur. The results of the given information follow the law of ......

Define the Law of Multiple Proportions.