A difficult problem in the synthesis of PGF$_2$$_\alpha$ is the introduction of the OH group at C15 in the desired configuration.
a. Label this stereogenic center as $R$ or $S$.
b. A well known synthesis of PGF$_2$$_\alpha$ involves reaction of $\textbf{A}$ with Zn(BH$_4)_2$, a metal hydride reagent similar in reactivity to NaBH$_4$, to form two isomeric products, $\textbf{B}$ and $\textbf{C}$. Draw their structures and indicate their stereochemical relationship.
c. Suggest a reagent to convert $\textbf{A}$ to the single stereoisomer $\textbf{X}$.