Final answer:
The lac repressor is active and binds to the operator to prevent transcription of the lac operon in the absence of lactose. It detaches when lactose is present, allowing the necessary genes to be expressed, which conserves energy and resources.
Step-by-step explanation:
The statement is true: The lac repressor protein is indeed active in the absence of lactose within the cell. The lac repressor binds to the operator region of the lac operon when lactose is not present, preventing RNA polymerase from transcribing the lac genes needed for lactose metabolism. When lactose is available, it is converted into allolactose, which binds to the lac repressor, causing a conformational change that releases the repressor from the operator. This release allows RNA polymerase to transcribe the genes needed for lactose digestion.
Expressing genes only when needed is beneficial because it conserves energy and resources. Producing enzymes that are not needed would be wasteful. Thus, the lac operon system is a highly efficient means of gene regulation that ensures enzymes for lactose digestion are produced only when lactose is present and needs to be metabolized.