Final answer:
When there is a mutation in both lacP and lacI, the lac operon will be expressed regardless of lactose presence, because the lacI gene product repressor can no longer bind to the operator to inhibit transcription.
Step-by-step explanation:
If there are mutations that inactivate lacP and lacI within the lac operon, the following is TRUE: C. The lac operon will be expressed regardless of lactose presence. The lacI gene encodes a repressor protein that, in the absence of lactose, binds to the operator to prevent transcription. If lacI is mutated and inactivated, the repressor cannot bind, and thus cannot block transcription of the operon. In addition, a mutation in lacP, the lac promoter, will affect the binding of RNA polymerase.
However, since the question directly addresses an inactive lacI mutation, it implies that RNA polymerase can still somehow bind to the promoter and transcribe the genes. With the repressor inactivated, these conditions lead to continuous transcription of the lac operon, whether lactose is present or not. A mutation in one of the structural genes of the lac operon would result in the loss of function for that gene product, but would not directly affect the operon's regulation.