Final answer:
The statement that repressor binding prevents RNA polymerase from binding to the promoter is false; the repressor binds to the operator, blocking transcription until lactose is present, which leads to dissociation of the repressor and allows gene expression.
Step-by-step explanation:
The statement that repressor binding prevents RNA polymerase from binding to the promoter in the lactose operon, and in the galactose operon, is false. In the repressor/operon model for regulating gene expression, the repressor binds not to the promoter but to the operator sequence, which is adjacent to or overlapping the promoter. This binding blocks RNA polymerase from transcribing the downstream structural genes.
When lactose is present, lactose or its isomer allolactose binds to the repressor, causing a conformational change that leads to the repressor dissociating from the operator. This allows RNA polymerase to bind to the promoter and transcribe the genes necessary for lactose digestion. In the case of a mutation in the repressor that prevents it from binding lactose, the repressor would remain bound to the operator, and the genes for lactose digestion would not be expressed, even in the presence of lactose.