A Research Group Working with E $\beta$ -Galactosidase Activity Under Different Environmental Conditions, as Shown in the Operon

A research group working with E. coli isolated several lac operon mutants. The group measured $\beta$ -galactosidase activity under different environmental conditions, as shown in the table below. Which statement draws a plausible conclusion about one of these mutants?
$$\begin{array} {c} { \beta \text { - galactosidase activity } } \\\begin{array} { | c | c | c | } \hline { \text { Mutant } } &\\ & \begin{array} { l } \text { Glucose present; } \\\text { lactose absent }\end{array} & \begin{array} { l } \text { Lactose present; } \\\text { glucose absent }\end{array} \\\hline \text { I } & 0 & 0 \\\hline \text { II } & + + + & + + + \\\hline \text { III } & 0 & + + + \\\hline \text { IV } & + + + & 0 \\\hline\end{array}\end{array}$$

A) Mutant I has an operator region that no longer binds repressor.
B) Mutant II has a repressor that no longer binds to the operator.
C) Mutant III has a promoter site that no longer binds RNA polymerase.
D) Mutant IV has a mutation in the $\beta$ -galactosidase gene, rendering its gene product inactive.

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