Compound A has the formula $\mathrm{C}_{8} \mathrm{H}_{8} .$ It reacts rapidly with $\mathrm{KMnO}_{4}$ to give
$\mathrm{CO}_{2}$ and a carboxylic acid, $\mathrm{B}\left(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{2}\right),$ but reacts with only 1 molar equivalent of $\mathrm{H}_{2}$ on catalytic hydrogenation over a palladium catalyst. On hydrogenation under conditions that reduce aromatic rings, 4 equivalents of $\mathrm{H}_{2}$ are taken up and hydrocarbon $\mathbf{C}\left(\mathrm{C}_{8} \mathrm{H}_{16}\right)$ is produced. What are the structures of $\mathrm{A}, \mathrm{B},$ and $\mathrm{C} ?$ Write the reactions.