The Accompanying Table Lists Several Genotypes Associated with the Lac $\beta$

The accompanying table lists several genotypes associated with the lac operon in E. coli. For each, indicate with a "+" or a "-" whether β-galactosidase would be expected to be produced at induced levels. Genotype                         $\beta$ -galactosidase production
                                        No Lactose         With Lactose
(a) $\quad I + O + Z + / F ^ { \prime } I + O + Z +$
(b) $\quad I - O c Z - / F ^ { \prime } I - O c Z -$
(c) $\quad I - O c Z + / F ^ { \prime } I - O + Z +$
(d) Is Oc $\mathrm { Z } - \mathrm { F } ^ { \prime }$ Is $\mathrm { O } + \mathrm { Z } ^ { + }$
$I ^ { + } =$ wild-type repressor
$I ^ { - } =$ mutant repressor (unable to bind to the operator)
Is $=$ mutant repressor (insensitive to lactose)
$\mathrm { O } ^ { + } =$ wild-type operator
$\mathrm { OC } =$ constitutive operator (insensitive to repressor)