Solution :
"Aldol" stands for the abbreviation, aldehyde and alcohol. When a ketone or an aldehyde's enolate reacts with the carbonyl of a molecule at the alpha carbon, under the acidic or basic conditions so as to obtained the ketone or β-hydroxy aldehyde, is known as an aldol reaction.
For the conversion of the aldol addition product of a 3-hydroxy-3-(4-nitrophenyl)-1-(2-pyridyl)-1-propanone to an aldol condensation product of (E)-3-(4-nitrophenyl)-1-(2-pyridyl)-1-propenone, the mechanism is given in the diagram a below :
