Final answer:
If a mutation inhibits the ability of RNA polymerase to bind to the lac operon, it would reduce the effectiveness of negative regulation and increase lac operon activity. Therefore, lac operon activity would increase.
Step-by-step explanation:
If a mutation inhibits the ability of RNA polymerase to bind to the lac operon, it would reduce the effectiveness of negative regulation and increase lac operon activity. This is because negative regulation occurs when the lac repressor protein binds to the operator sequence, preventing RNA polymerase from binding to the promoter and transcribing the structural genes. However, if RNA polymerase cannot bind to the lac operon due to the mutation, the lac operon will not be effectively repressed and more lactose-metabolizing enzymes will be produced. Therefore, lac operon activity would increase.