State whether the following statements are True or False:
$(1)$ The oxidation number of nitrogen in ammonium chloride $(NH_4Cl)$ is $(-3)$.
$(2)$ The oxidation number of $C$ in methyl chloride $(CH_3Cl)$ is $(-2)$.
$(3)$ In the following reaction,the oxidation number of $Br$ changes from $0$ to $+5$: $Br_2 \to BrO_3^-$.

(A) $(1)$ True: In $NH_4Cl$,the oxidation state of $N$ is $x + 4(+1) + (-1) = 0$,so $x + 3 = 0$,$x = -3$.
$(2)$ False: In $CH_3Cl$,let the oxidation state of $C$ be $x$. $x + 3(+1) + (-1) = 0$,so $x + 2 = 0$,$x = -2$. Wait,the statement says $-2$,which is correct. Let's re-evaluate: $x + 3 - 1 = 0 \implies x = -2$. The statement is True.
$(3)$ True: In $Br_2$,the oxidation state of $Br$ is $0$. In $BrO_3^-$,$x + 3(-2) = -1 \implies x - 6 = -1 \implies x = +5$. The statement is True.