Identify the product formed when vapours of $2-$methylpropan$-2-$ol are passed over hot copper.

The dehydration of alcohols is an example of ...... .

The reagent used for the dehydration of an alcohol is

$CH_3-CH(OH)-CH_3$ $\xrightarrow{PBr_3} X$ $\xrightarrow{Mg/\text{ether}} Y$ $\xrightarrow{H_2O/H^+} \text{The final product is}$

Describe the reactions of alcohols with $(a)$ $HX$ and Lucas test,$(b)$ $PX_3$,and $(c)$ dehydration reactions.

Given below are two statements :
Statement $I$ :
In Lucas test,primary,secondary and tertiary alcohols are distinguished on the basis of their reactivity with conc. $HCl + ZnCl_{2}$,known as Lucas Reagent.
Statement $II$ :
Primary alcohols are most reactive and immediately produce turbidity at room temperature on reaction with Lucas Reagent.
In the light of the above statements,choose the most appropriate answer from the options given below :