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We know that cyclopropyl, because of $\ce{sp^{\sim 5}}$, hybrid orbitals behaves much like a double bond. It even takes part in conjugation to stabilise positive charge on carbons adjacent to it. I would like to know if it conjugates with the carbonyl carbon too?

Are there cases of 1,4 addition and 1,2 addition with such compounds analogous to that observed in alpha-beta unsaturated carbonyl compounds?

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