Predict what would happen in the lac operon for each of these scenarios lactose is present glucose is scarce

Some things to clarify: 
1. The lac operon codes not only for lactase, but also for a lac operon repressor. This repressor works as a negative control and binds the operon's regulatory site to repress transcription at all times if lactose is not present. When lactose is present, the repressor is not able to bind to the regulatory site and allows for transcription. This is because lactose binds with the repressor itself and therefore does not allow it to bind the regulatory site.
2. Glucose is the preferred carbon source, and has a positive control mechanism so that when glucose is around, the lac operon is off and vice versa. When glucose is not present, cAMP (cyclic AMP) binds with CAP (catabolite activator protein) and this cAMP/CAP complex binds to the regulatory site of the lac operon to allow transcription (enhancement) of the lac operon. When glucose is present, glucose inhibits an enzyme responsible for the formation of cAMP. Without cAMP being produced, the cAMP/CAP complex cannot enhance transcription of the operon.

+ glucose/+ lactose: Lac operon would be off. This is because the cAMP/CAP  complex is not bound to the regulatory site.
+ glucose/- lactose: Lac operon would be off. This is because the lac operon repressor is bound to the regulatory site.
- glucose/- lactose: Lac operon would be off. Despite the fact that the cAMP/CAP complex is bound, transcription still cannot occur because the lac operon repressor is bound to the regulatory site.
- glucose/+ lactose: Lac operon would be on. This is because the cAMP/CAP complex is bound and lactose is inhibiting the binding of the lac operon repressor molecule, allowing for transcription of the operon.

Bis the correct answer.