Final answer:
If both glucose and lactose are absent, the lac operon will remain in a repressed state because lactose is needed to remove the repressor and allow transcription.
Step-by-step explanation:
If glucose is absent, but so is lactose, the lac operon will be repressed. This is because the operon requires lactose to be present in order to induce transcription. In the absence of lactose, the repressor protein remains bound to the operator, preventing transcription. Even if glucose is also absent, which normally allows CAP to enhance transcriptional activation, lactose absence ensures that the repressor is in place, keeping the operon off. Therefore, with no glucose and no lactose, the operon will not be induced and will remain in a repressed state.