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Treatment of cyclopentane-1,3-dione with a base followed by addition of methyl iodide affords a mixtures of...

Treatment of cyclopentane-1,3-dione with a base followed by addition of methyl iodide affords a mixtures of 2-methylcyclopentane-1,3-dione, 2,2-dimethylcyclopentane-1,3-dione and 3-methoxy-2-cyclopenten-1-one. Explain with the aid of a mechanism how each product is formed.

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