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 β-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.