Lac operon is an example of

The correct option is "both positive and negative regulation".

The regulation of the lac operon (lactose operon) in Escherichia coli is a classic example of gene regulation that involves both negative control and positive control mechanisms to ensure efficient energy utilization.

1. Negative Regulation:
The lac operon is normally kept in an "off" state by a repressor protein, which is encoded by the regulatory gene lacI.
When lactose is absent, the active repressor protein binds to the operator region ($o$) of the operon. This binding physically blocks RNA polymerase from transcribing the structural genes ($lacZ$, $lacY$, and $lacA$).
When lactose is present, it is converted into allolactose (the inducer). Allolactose binds to the repressor protein, altering its shape so that it can no longer bind to the operator. This removes the blockade, allowing transcription to occur. Because the system is turned on by disabling a repressor, this control mechanism is referred to as negative regulation.

2. Positive Regulation:
Even in the presence of lactose, transcription of the operon is very low if glucose (the cell's preferred energy source) is also available.
When glucose levels are low, the concentration of cyclic AMP (cAMP) inside the cell increases.
cAMP binds to an activator protein called Catabolite Activator Protein (CAP), also known as cAMP Receptor Protein (CRP).
The active cAMP-CAP complex binds to a specific promoter site on the DNA, which enhances the binding affinity of RNA polymerase to the promoter, significantly boosting transcription. Because the binding of an activator protein (CAP) directly promotes transcription, this mechanism is called positive regulation.

Therefore, because both a repressor (negative control) and an activator (positive control) are involved in its operation, the lac operon is an example of both positive and negative regulation.