The correct option is C Both A and B
Repressors are the transcription factors that bind to operator gene and prevent the RNA polymerase from binding the downstream promoter genes and thus prevent their transcription. The inducer is a molecule that binds to the repressor and causes conformational changes in repressor which in turn can no longer bind to the operator. In presence of lactose, allolactose; an isomer of lactose, binds to the repressor and causes an allosteric shift. The altered repressor cannot bind to the operator, allowing RNA polymerase to transcribe the lac genes. Thus, allolactose serves as an inducer of lac operon whereas in absence lactose repressor binds to the operator and thus inhibit the protein synthesis. Thus, the correct answer is option C.