For each of the following reactions, draw the major elimination product; if the product can exist as stereoisomers, indicate which stereoisomer is obtained greater yield.
a. $(R)$ -2-bromohexane $+$ high concentration of $\mathrm{CH}_{3} \mathrm{O}^{-}$
b. $(R)-3$ -bromo- 3 -methylhexane $+\mathrm{CH}_{3} \mathrm{OH}$
c. trans-1-chloro-2-methylcyclohexane + high concentration of $\mathrm{CH}_{3} \mathrm{O}^{-}$
d. trans-1-chloro-3-methylcyclohexane + high concentration of $\mathrm{CH}_{3} \mathrm{O}^{-}$
e. 3 -bromo- 3 -methylpentane $+$ high concentration of $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{O}^{-}$
f. 3 -bromo- 3 -methylpentane $+\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}$