A sample of $(R)-\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}\left(\mathrm{CH}_{3}\right) \mathrm{Cl}$ reacts with
$\mathrm{CH}_{3} \mathrm{O}^{-}$ in dimethyl sulfoxide, $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{SO},$ a convenient solvent for organic reactions. The resulting solution is optically active. (a) Write the formula of the product. (b) By which mechanism does this nucleophilic substitution reaction occur?