The following hypothetical genotypes have genes A, B, and C corresponding to lacI, lacO, and lacZ, but not necessarily in that order. Data in the table indicate whether -galactosidase is produced in the presence and absence of the inducer for each genotype. Use these data to identify the correspondence between A, B, and C and the lacI, lacO, and lacZ genes. Carefully explain your reasoning for identifying each gene.

Genotype                  β-Galactosidase Production
                             Inducer Present       Inducer Absent
1. A⁻B⁺C⁺⁻                          +                              +
2. A⁺B⁺C⁻                           +                              +
3.A⁻B⁺C⁺/A⁺B⁺C⁺                +                              +
4. A⁺B⁺C/A⁺B⁺C⁺⁻                +                              –