Draw the product obtained by heating each pair of ketones in a basic solution.

Heating the ketone (a) given is done by following these steps:

• First, align the$\alpha ,\beta$ -unsaturated carbonyl compound (but-3-en-2-one)so that the carbonyl oxygen points at seven o’clock and the double bond is at the top of the structure.
• Draw the dicarbonyl compound (2-methylcyclohexane-1,3-dione) to the right of the first with one ketone carbonyl oxygen also pointing at seven o’clock and the other pointing at noon.
• Connectthe two pairs of carbons and draw the double bond that forms as a result of dehydration,resulting in the formation of 8a-methyl-3,4,8,8a-tetrahydronapthalene-1,6(2H,7H)-dioneshowed as follows:

Formation of 8a-methyl-3,4,8,8a-tetrahydronapthalene-1,6(2H,7H)-dione

Heating the ketone (b) given is done by following these steps:

• First, align the$\alpha ,\beta$ -unsaturated carbonyl compound (E)-hex-4-en-3-oneso that the carbonyl oxygen points at seven o’clock and the double bond is at the top of the structure.
• Draw the cyclopentanonecompound to the right of the first with one ketone carbonyl oxygen also pointing at seven o’clock.
• Connectthe two pairs of carbons and draw the double bond that forms as a result of dehydration, resulting in the formation of 4,7-dimethyl-2,3,7,7a-tetrahydro-1H-inden-5(6H)-oneshown as follows:

Formationof 4,7-dimethyl-2,3,7,7a-tetrahydro-1H-inden-5(6H)-one