Why do the cells transformed with puc18 and plasmid lux grow in the presence of ampicillin?

The bacterial cells transformed with PUC18 and plasmid lux grow in the presence of ampicillin, because the DNA of bacterial cells had incorporated parts of plasmid DNA and became ampicillin resistant.

Explanation:

The bacteria showing this property is mainly known as Escherichia coli (E. coli). These bacteria cells generally shows no growth in presence of antibiotic like ampicillin. Whereas when these cells are treated with PUC 18 and plasmid lux, then the bacterial DNA undergo certain transformation due to incorporation of strands of DNA of plasmid into them. This transformation make them resistance to ampicillin, when they are cultured in agar media with ampicillin in it.

during the process of dna replication, brdu can replace thymidine and incorporate into the newly synthesized dna, cell proliferation thus can be reflected in the extent of brdu incorporation.