You have found two compounds, A and B, in an abandoned government lab. Both compounds appear the same to the naked eye, and are only labeled C7H12O. After extensive tests you determine that the compounds have identical physical properties (e.g., mp, bp, index of refraction), but they appear to be optically active samples that rotate plane polarized light (ppl) in opposite directions with equal magnitude. Reduction of either A or B gives 1-methylcyclohexanol. Hydrolysis of A under acidic and basic conditions gives two different compounds, C and D, respectively, that are optically active, but rotate ppl in opposite directions with equal magnitude. Interestingly, hydrolysis of B under the same two sets of conditions yields the same two compounds, C and D, but with opposite results: basic conditions yields C and acidic conditions yields D. Treatment of either C or D with periodic acid yields the same dicarbonyl compound shown. Finally, treatment of A and B with methylmagnesium bromide followed by acidic workup yields two different compounds, E and F, which are also related by their rotating ppl in opposite directions with equal magnitude, but otherwise have identical physical properties. Treatment of E and F with H2SO4 yields 1,2-dimethylcyclohexene. Based on these observations, provide structures for compounds A through F.