If you mutate lacI so that the repressor cannot bind lactose or other inducers any more (LacI-s), will this mutant be able to use lactose?

this mutant will not be able to use lactose

Explanation:

The lac operon is a cluster of genes with the same promoter which are transcribed as a single messenger RNA (mRNA). The lac operon encodes different enzymes that are used by the bacteria to obtain energy from lactose. The LacI gene is required for producing a repressor protein that binds to the promoter of the operon in order to inactivate its transcription (i.e., by preventing RNA polymerase from binding). A mutation in this gene prevents from its binding to lactose and it becomes inactive to the Lac operon.

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