Show how you would accomplish each of the following synthetic conversions.

A carbene insertion reaction is the insertion of carbene into an electron-rich pi double bond of an alkene. This reaction is a concerted reaction that occurs in a single step only

Trans-2-butene reacts with methylene iodide; the zinc-copper couple gives trans-cyclopropane as the product. This reaction is known as the Simmons-Smith reaction. This reaction is stereospecific, meaning trans-alkene will get converted to trans-cyclopropane, and cis-alkene will get converted to cis-cyclopropane.

Alkene to cycloalkane

Sodium hydroxide on reaction with methylene bromide produces carbene, singlet carbene. This singlet carbene will then undergo an insertion reaction at the double bond of cyclopentene and forms bromocyclopropane. In that process, one bromide ion acts as a leaving group.

Cyclohexanol, on reaction with sulphuric acid followed by heating, undergoes dehydration, loss of water molecule and produces cyclohexene as the product. Then, further on reaction with trichloromethane and a base such as sodium hydroxide, a singlet carbene is produced, which undergoes insertion reaction at the double bond and forms chlorocyclopropane as the product with the loss of one chloride ion, which acts as a leaving group.