In Order to Analyze How Different Components of the Lac $\beta$

In order to analyze how different components of the lac operon work, scientists created special strains of E. coli, called partial diploids. A partial diploid has one full copy of the lac operon in the bacterial chromosome plus another copy of the lac operon in a plasmid. Hence, for the lac operon (and only the lac operon) the bacterial cell is a diploid. Below is one possible genotype of a partial diploid. The genotype written to the left of the slash (/) is that of the lac operon in the bacterial chromosome, and the genotype written to the right of the slash is that of the lac operon in the plasmid. I⁺ P⁺ O^c Z⁺/ I^- P^- O⁺ Z^-
For the partial diploid genotype shown here, determine whether functional $\beta$ -galactosidase is synthesized in the absence and in the presence of lactose (and the accompanying allolactose that is the actual inducer) .

A) $\beta$ -galactosidase is produced whether lactose is present or absent.
B) $\beta$ -galactosidase is not produced whether lactose is present or absent.
C) $\beta$ -galactosidase is produced when lactose is present but is not produced when lactose is absent.
D) $\beta$ -galactosidase is not produced when lactose is present but is produced when lactose is absent.