An unknown hydrocarbon A with the formula $\mathrm{C}_{6} \mathrm{H}_{12}$ reacts with 1 molar equivalent of $\mathrm{H}_{2}$ over a palladium catalyst. Hydrocarbon $\mathrm{A}$ also reacts with OsO_ to give diol B. When oxidized with KMnO_in acidic solution, A gives two fragments. One fragment is propanoic acid, $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CO}_{2} \mathrm{H},$ and the other fragment is ketone $\mathbf{C .}$ What are the structures of $\mathbf{A}, \mathbf{B},$ and $\mathbf{C} ?$ Write all reactions, and show your reasoning.