Step 1: Understanding the Concept:
The starting material is acetone cyanohydrin. This molecule contains both a hydroxyl group (\(-\text{OH}\)) and a nitrile group (\(-\text{CN}\)). The reactions involve functional group transformations of the nitrile group.
Step 2: Detailed Explanation:
Formation of Product A:
Acetone cyanohydrin is treated with \(\text{LiAlH}_4\), which is a powerful reducing agent. It reduces the nitrile (\(-\text{CN}\)) group to a primary amine (\(-\text{CH}_2\text{NH}_2\)) group. The alcohol group remains unchanged.
\[ \text{(CH}_3\text{)}_2\text{C(OH)CN} \xrightarrow{\text{LiAlH}_4 / \text{H}_3\text{O}^+} \text{(CH}_3\text{)}_2\text{C(OH)CH}_2\text{NH}_2 \]
Thus, A is 1-amino-2-methylpropan-2-ol.
Formation of Product B:
The nitrile group undergoes acidic hydrolysis when treated with \(\text{H}_3\text{O}^+\) and \(\text{H}_2\text{SO}_4\). Complete hydrolysis of a nitrile group yields a carboxylic acid group (\(-\text{COOH}\)).
\[ \text{(CH}_3\text{)}_2\text{C(OH)CN} \xrightarrow{\text{H}_3\text{O}^+ / \text{H}_2\text{SO}_4} \text{(CH}_3\text{)}_2\text{C(OH)COOH} \]
Thus, B is 2-hydroxy-2-methylpropanoic acid (also known as \(\alpha\)-hydroxyisobutyric acid).
Step 3: Final Answer:
Comparing the chemical logic with the provided options, Option (D) represents the correct structures.