Question #44995

An aqueous solution of a naturally occurring, non-reducing disaccharide $\mathbf{X}$ ($\ce{C12H22O11}$) is hydrolyzed with dilute $\ce{H2SO4}$ to yield a single D-aldohexose $\mathbf{Y}$. $\mathbf{Y}$ forms an osazone identical to that formed by D-fructose. $\mathbf{Y}$ is subjected to the following reaction sequence: $\mathbf{Y} \xrightarrow[2. \ \ce{H3O^+}, \ \Delta \quad 3. \ \ce{Na(Hg)}, \ \ce{H2O}, \ pH \ 3-5]{1. \ \ce{HCN}} \mathbf{P} + \mathbf{Q}$ where $\mathbf{P}$ and $\mathbf{Q}$ are isomeric aldoheptoses. Subsequent oxidation of $\mathbf{P}$ and $\mathbf{Q}$ with warm concentrated $\ce{HNO3}$ yields heptaric acids $\mathbf{P'}$ and $\mathbf{Q'}$, respectively. Which of the following correctly describes the stereochemical relationship between $\mathbf{P}$ and $\mathbf{Q}$, and the optical activity of $\mathbf{P'}$ and $\mathbf{Q'}$?