Given are the two cleavage reactions:

(i) ${\left({\mathrm{CH}}_3\right)}_3{\mathrm{COCH}}_3\to {\mathrm{CH}}_3\mathrm{I}+{\left({\mathrm{CH}}_3\right)}_3\mathrm{COH}$

(ii) ${\left({\mathrm{CH}}_3\right)}_3{\mathrm{COCH}}_3\to {\mathrm{CH}}_3\mathrm{OH}+{\left({\mathrm{CH}}_3\right)}_3\mathrm{CI}$

Which of the following statements is correct?

The low polarity of solvent ether favors the ${\mathrm{S}}_{\mathrm{N}}2$ mechanism and the high polarity of solvent water favours ${\mathrm{S}}_{\mathrm{N}}1$ mechanism.

The mechanism is $$\begin{gathered} {\left({\mathrm{CH}}_3\right)}_3{\mathrm{COCH}}_3+\mathrm{HI}\to {\left({\mathrm{CH}}_3\right)}_3\mathrm{C}\underset{|}{\stackrel{+}{\mathrm{O}}}{\mathrm{CH}}_3+\mathrm{\Gamma } \\ \mathrm{H} \end{gathered}$$

$$\begin{gathered} {\mathrm{S}}_{\mathrm{N}}1: {\left({\mathrm{CH}}_3\right)}_3\mathrm{C}\underset{|}{\stackrel{+}{\mathrm{O}}}{\mathrm{CH}}_3\to {\mathrm{CH}}_3\mathrm{OH}+{\left({\mathrm{CH}}_3\right)}_3{\mathrm{C}}^{+}\stackrel{{\mathrm{I}}^{-}}{⟶}{\left({\mathrm{CH}}_3\right)}_3\mathrm{CI}; \\ \mathrm{H} \end{gathered}$$

$$\begin{gathered} {\mathrm{S}}_{\mathrm{N}}2:\mathrm{\Gamma }+{\left({\mathrm{CH}}_3\right)}_3\mathrm{C}\underset{|}{\stackrel{+}{\mathrm{O}}}{\mathrm{CH}}_3\to {\mathrm{CH}}_3\mathrm{I}+\mathrm{HOC}{\left({\mathrm{CH}}_3\right)}_3 \\ \mathrm{H} \end{gathered}$$