Pushpa K. answered 04/10/16
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You are correct. Lac P is the promoter region of the lac operon that consists of RNA polymerase binding site and the regulatory sequences/elements to which regulatory proteins bind and control the expression of the lac structural genes Lac Z, Lac Y and Lac A.
In the absence of lactose, a repressor protein bound at the operator site in the promoter region prevents RNA polymerase from transcribing lac operon genes, so the lac operon is turned off and the lac genes are not expressed.
In the presence of lactose, a small amount of lactose is absorbed by the bacteria and converted to allolactose which binds to the repressor protein and causes change in its shape/conformation in such a way that it is unable to bind at the operator site.
Absence of the repressor protein at the operator site enables RNA polymerase to transcripe lac operaon genes provided an activator protein (catabolite activator protein in complex with cyclic AMP molecule) is bound at it's binding site in the promoter.
So the absence of the repressor protein binding and the binding of the activator protein at the promoter turns the transcription of lac operon genes on.
Hope this helps.