Four independent lac⁻ mutants (mutants A to D) are isolated in haploid strains of E. coli. The strains have the following phenotypic characteristics:

Mutant A is lac⁻, but transcription1 of operon genes is induced by lactose.
Mutant B is lac⁻ and has uninducible2 transcription of operon genes.
Mutant C is lac⁺ and has constitutive3 transcription of operon genes.
Mutant D is lac⁺ and has constitutive3 transcription of operon genes.

A microbiologist develops donor and recipient varieties of each mutant strain and crosses them with the results shown below. The table indicates whether inducible, constitutive, or noninducible transcription occurs, along with  and  growth habit for each partial diploid. Assume each strain has a single mutation.

Mating             Transcription and Growth
A × B                 lac⁻
A × C                 lac⁺, inducible
A × D                 lac⁺, constitutive
B × C                 lac⁺, inducible
B × D                 lac⁺, constitutive
C × D                 lac⁺, constitutive

Use this information to identify which lac operon gene is mutated in each strain.