2-Methylbutene can be formed by dehydrating two different compounds (A and B) of molecular formula $\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O} .$ When $\mathbf{A}$ is mildly oxidized, compound $\mathbf{C}$ $\left(\mathrm{C}_{5} \mathrm{H}_{10} \mathrm{O}\right)$ forms, which can be oxidized further to a carboxylic acid. When compound B undergoes dehydration, 2-methylbutene is formed as the minor product. In addition, compound B cannot be oxidized further. Use this information to determine the identity of compounds $\mathbf{A}, \mathbf{B},$ and $\mathbf{C}$.